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1,642 results on '"Schwarz, Benjamin"'

1. Jamaican fruit bat (Artibeus jamaicensis) insusceptibility to mucosal inoculation with SARS-CoV-2 Delta variant is not caused by receptor compatibility

Author

Port, Julia R., Riopelle, Jade C., van Tol, Sarah, Wickenhagen, Arthur, Bohrnsen, Eric, Sturdevant, Daniel E., Rosenke, Rebecca, Lovaglio, Jamie, Lack, Justin, Anzick, Sarah L., Cordova, Kathleen, Yinda, Kwe Claude, Hanley, Patrick W., Schountz, Tony, Kendall, Lon V., Shaia, Carl I., Saturday, Greg, Martens, Craig, Schwarz, Benjamin, and Munster, Vincent J.

Published
2024
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3. GIMAP5 deficiency reveals a mammalian ceramide-driven longevity assurance pathway

Author

Park, Ann Y., Leney-Greene, Michael, Lynberg, Matthew, Gabrielski, Justin Q., Xu, Xijin, Schwarz, Benjamin, Zheng, Lixin, Balasubramaniyam, Arasu, Ham, Hyoungjun, Chao, Brittany, Zhang, Yu, Matthews, Helen F., Cui, Jing, Yao, Yikun, Kubo, Satoshi, Chanchu, Jean Michel, Morawski, Aaron R., Cook, Sarah A., Jiang, Ping, Ravell, Juan C., Cheng, Yan H., George, Alex, Faruqi, Aiman, Pagalilauan, Alison M., Bergerson, Jenna R. E., Ganesan, Sundar, Chauvin, Samuel D., Aluri, Jahnavi, Edwards-Hicks, Joy, Bohrnsen, Eric, Tippett, Caroline, Omar, Habib, Xu, Leilei, Butcher, Geoffrey W., Pascall, John, Karakoc-Aydiner, Elif, Kiykim, Ayca, Maecker, Holden, Tezcan, İlhan, Esenboga, Saliha, Heredia, Raul Jimenez, Akata, Deniz, Tekin, Saban, Kara, Altan, Kuloglu, Zarife, Unal, Emel, Kendirli, Tanıl, Dogu, Figen, Karabiber, Esra, Atkinson, T. Prescott, Cochet, Claude, Filhol, Odile, Bosio, Catherine M., Davis, Mark M., Lifton, Richard P., Pearce, Erika L., Daumke, Oliver, Aytekin, Caner, Şahin, Gülseren Evirgen, Aksu, Aysel Ünlüsoy, Uzel, Gulbu, Koneti Rao, V., Sari, Sinan, Dalgıç, Buket, Boztug, Kaan, Cagdas, Deniz, Haskologlu, Sule, Ikinciogullari, Aydan, Schwefel, David, Vilarinho, Silvia, Baris, Safa, Ozen, Ahmet, Su, Helen C., and Lenardo, Michael J.

Published
2024
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4. Author Correction: GIMAP5 deficiency reveals a mammalian ceramide-driven longevity assurance pathway

Author

Park, Ann Y., Leney-Greene, Michael, Lynberg, Matthew, Gabrielski, Justin Q., Xu, Xijin, Schwarz, Benjamin, Zheng, Lixin, Balasubramaniyam, Arasu, Ham, Hyoungjun, Chao, Brittany, Zhang, Yu, Matthews, Helen F., Cui, Jing, Yao, Yikun, Kubo, Satoshi, Chanchu, Jean Michel, Morawski, Aaron R., Cook, Sarah A., Jiang, Ping, Ravell, Juan C., Cheng, Yan H., George, Alex, Faruqi, Aiman, Pagalilauan, Alison M., Bergerson, Jenna R. E., Ganesan, Sundar, Chauvin, Samuel D., Aluri, Jahnavi, Edwards-Hicks, Joy, Bohrnsen, Eric, Tippett, Caroline, Omar, Habib, Xu, Leilei, Butcher, Geoffrey W., Pascall, John, Karakoc-Aydiner, Elif, Kiykim, Ayca, Maecker, Holden, Tezcan, İlhan, Esenboga, Saliha, Heredia, Raul Jimenez, Akata, Deniz, Tekin, Saban, Kara, Altan, Kuloglu, Zarife, Unal, Emel, Kendirli, Tanıl, Dogu, Figen, Karabiber, Esra, Atkinson, T. Prescott, Cochet, Claude, Filhol, Odile, Bosio, Catherine M., Davis, Mark M., Lifton, Richard P., Pearce, Erika L., Daumke, Oliver, Aytekin, Caner, Şahin, Gülseren Evirgen, Aksu, Aysel Ünlüsoy, Uzel, Gulbu, Koneti Rao, V., Sari, Sinan, Dalgıç, Buket, Boztug, Kaan, Cagdas, Deniz, Haskologlu, Sule, Ikinciogullari, Aydan, Schwefel, David, Vilarinho, Silvia, Baris, Safa, Ozen, Ahmet, Su, Helen C., and Lenardo, Michael J.

Published
2024
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13. Fecal transplant from vaginally seeded infants decreases intraabdominal adiposity in mice

Author

Namasivayam, Sivaranjani, primary, Tilves, Curtis, additional, Ding, Hua, additional, Wu, Shaoguang, additional, Domingue, Jada C, additional, Ruiz-Bedoya, Camilo, additional, Shah, Ankit, additional, Bohrnsen, Eric, additional, Schwarz, Benjamin, additional, Bacorn, Mickayla, additional, Chen, Qing, additional, Levy, Shira, additional, Dominguez Bello, Maria Gloria, additional, Jain, Sanjay K, additional, Sears, Cynthia L, additional, Mueller, Noel T, additional, and Hourigan, Suchitra K, additional

Published
2024
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16. Nudt21 Controls Cell Fate by Connecting Alternative Polyadenylation to Chromatin Signaling

Author

Brumbaugh, Justin, Di Stefano, Bruno, Wang, Xiuye, Borkent, Marti, Forouzmand, Elmira, Clowers, Katie J, Ji, Fei, Schwarz, Benjamin A, Kalocsay, Marian, Elledge, Stephen J, Chen, Yue, Sadreyev, Ruslan I, Gygi, Steven P, Hu, Guang, Shi, Yongsheng, and Hochedlinger, Konrad

Subjects
Biological Sciences, Biomedical and Clinical Sciences, Medical and Health Sciences, Developmental Biology, Biological sciences, Biomedical and clinical sciences
Abstract

(Cell 172, 106–120; January 11, 2018) Due to a production error, the original publication of this article included typographic errors in Figure 1. In that figure, four instances of “THY-1” appeared as “HY-1”. These errors have been corrected in print and online, and we apologize for any inconvenience. [Figure presented] A Serial siRNA Screen Identifies Nudt21 as a Potent Barrier to Reprogramming (corrected) [Figure presented] A Serial siRNA Screen Identifies Nudt21 as a Potent Barrier to Reprogramming (original)

Published
2018

18. Cell restriction factors, and not receptor compatibility, block Jamaican fruit bat (Artibeus jamaicensis) susceptibility to mucosal inoculation with SARS-CoV-2 Delta variant

Author

Port, Julia R., primary, Riopelle, Jade C., additional, Tol, Sarah van, additional, Wickenhagen, Arthur, additional, Bohrnsen, Eric, additional, Sturdevant, Daniel E., additional, Rosenke, Rebecca, additional, Lovaglio, Jamie, additional, Lack, Justin, additional, Anzick, Sarah L., additional, Cordova, Kathleen, additional, Yinda, Kwe Claude, additional, Hanley, Patrick W., additional, Schountz, Tony, additional, Kendall, Lon V., additional, Shaia, Carl I., additional, Saturday, Greg, additional, Martens, Craig, additional, Schwarz, Benjamin, additional, and Munster, Vincent J., additional

Published
2024
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24. Bessel operators on Jordan pairs and small representations of semisimple Lie groups

Author

Möllers, Jan and Schwarz, Benjamin

Subjects
Mathematics - Representation Theory
Abstract

We provide a uniform construction of $L^2$-models for all small unitary representations in degenerate principal series of semisimple Lie groups which are induced from maximal parabolic subgroups with abelian nilradical. This generalizes previous constructions to the case of a maximal parabolic subgroup which is not necessarily conjugate to its opposite, and hence the previously used Jordan algebra methods have to be generalized to Jordan pairs. The crucial ingredients for the construction of the $L^2$-models are the Lie algebra action and the spherical vector. Working in the so-called Fourier transformed picture of the degenerate principal series, the Lie algebra action is given in terms of Bessel operators on Jordan pairs. We prove that precisely for those parameters of the principal series where small quotients occur, the Bessel operators are tangential to certain submanifolds. Further, we show that the small quotients are unitarizable if and only if these submanifolds carry equivariant measures. In this case we can express the spherical vectors in terms of multivariable K-Bessel functions, and some delicate estimates for these Bessel functions imply the existence of the $L^2$-models., Comment: 50 pages

Published
2016

26. Higher Laplacians on pseudo-Hermitian symmetric spaces

Author

Schwarz, Benjamin

Subjects
Mathematics - Representation Theory, Mathematics - Differential Geometry, 32A50 (Primary) 53C35, 32M15, 22E46 (Secondary)
Abstract

Let $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each positive integer $m$, which generalize the ordinary Laplace-Beltrami operator. We show that $L_1,L_3,\ldots, L_{2r-1}$ form a set of algebraically independent generators for the algebra $\mathbb{D}_G(X)$ of $G$-invariant differential operators on $X$, where $r$ denotes the rank of $X$. This confirms a conjecture of Engli\v{s} and Peetre, originally stated for the class of Hermitian symmetric spaces., Comment: 26 pages

Published
2014

29. Reversible histone deacetylase activity catalyzes lysine acylation

Author

Tsusaka, Takeshi, primary, Najar, Mohd. Altaf, additional, Schwarz, Benjamin, additional, Bohrnsen, Eric, additional, Oses-Prieto, Juan A., additional, Lee, Christina, additional, Burlingame, Alma L., additional, Bosio, Catharine M., additional, Burslem, George M., additional, and Goldberg, Emily L., additional

Published
2023
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30. Lipin-1 restrains macrophage lipid synthesis to promote inflammation resolution.

Author

Bamgbose, Temitayo T., primary, Schilke, Robert M., additional, Igiehon, Oluwakemi O., additional, Nkadi, Ebubechukwu H., additional, Custis, David, additional, Bharrhan, Sushma, additional, Schwarz, Benjamin, additional, Bohrnsen, Eric, additional, Bosio, Catharine, additional, Scott, Rona S., additional, Yurdagul, Arif, additional, Finck, Brian, additional, and Woolard, Matthew, additional

Published
2023
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31. Sex differences and individual variability in the captive Jamaican fruit bat (Artibeus jamaicensis) intestinal microbiome and metabolome

Author

Riopelle, Jade C, primary, Shamsaddini, Amirhossein, additional, Holbrook, Myndi G, additional, Bohrnsen, Eric, additional, Lovaglio, Jamie, additional, Cordova, Kathleen, additional, Hanley, Patrick, additional, Lon, Kendall V, additional, Bosio, Catherine M, additional, Schountz, Tony, additional, Schwarz, Benjamin, additional, Munster, Vincent J, additional, and Port, Julia R, additional

Published
2023
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32. Hilbert series of nearly holomorphic sections on generalized flag manifolds

Author

Schwarz, Benjamin

Subjects
Mathematics - Representation Theory, Mathematics - Complex Variables, Primary 32A50, Secondary 32L10, 14M15, 22E46
Abstract

Let X=G/P be a complex flag manifold and E->X be a G-homogeneous holomorphic vector bundle. Fix a U-invariant Kaehler metric on X with U in G maximal compact. We study the sheaf of nearly holomorphic sections and show that the space of global nearly holomorphic sections in E coincides with the space of U-finite smooth sections in E. The degree of nearly holomorphic sections defines a U-invariant filtration on this space. Using sheaf cohomology, we determine in suitable cases the corresponding Hilbert series. It turns out to be given in terms of Lusztig's q-analog of Kostant's weight multiplicity formula., Comment: 18 pages, typos corrected, minor changes

Published
2014

35. Global data on earthworm abundance, biomass, diversity and corresponding environmental properties

Author

Phillips, Helen R. P., Bach, Elizabeth M., Bartz, Marie L. C., Bennett, Joanne M., Beugnon, Rémy, Briones, Maria J. I., Brown, George G., Ferlian, Olga, Gongalsky, Konstantin B., Guerra, Carlos A., König-Ries, Birgitta, Krebs, Julia J., Orgiazzi, Alberto, Ramirez, Kelly S., Russell, David J., Schwarz, Benjamin, Wall, Diana H., Brose, Ulrich, Decaëns, Thibaud, Lavelle, Patrick, Loreau, Michel, Mathieu, Jérôme, Mulder, Christian, van der Putten, Wim H., Rillig, Matthias C., Thakur, Madhav P., de Vries, Franciska T., Wardle, David A., Ammer, Christian, Ammer, Sabine, Arai, Miwa, Ayuke, Fredrick O., Baker, Geoff H., Baretta, Dilmar, Barkusky, Dietmar, Beauséjour, Robin, Bedano, Jose C., Birkhofer, Klaus, Blanchart, Eric, Blossey, Bernd, Bolger, Thomas, Bradley, Robert L., Brossard, Michel, Burtis, James C., Capowiez, Yvan, Cavagnaro, Timothy R., Choi, Amy, Clause, Julia, Cluzeau, Daniel, Coors, Anja, Crotty, Felicity V., Crumsey, Jasmine M., Dávalos, Andrea, Cosín, Darío J. Díaz, Dobson, Annise M., Domínguez, Anahí, Duhour, Andrés Esteban, van Eekeren, Nick, Emmerling, Christoph, Falco, Liliana B., Fernández, Rosa, Fonte, Steven J., Fragoso, Carlos, Franco, André L. C., Fusilero, Abegail, Geraskina, Anna P., Gholami, Shaieste, González, Grizelle, Gundale, Michael J., López, Mónica Gutiérrez, Hackenberger, Branimir K., Hackenberger, Davorka K., Hernández, Luis M., Hirth, Jeff R., Hishi, Takuo, Holdsworth, Andrew R., Holmstrup, Martin, Hopfensperger, Kristine N., Lwanga, Esperanza Huerta, Huhta, Veikko, Hurisso, Tunsisa T., Iannone, III, Basil V., Iordache, Madalina, Irmler, Ulrich, Ivask, Mari, Jesús, Juan B., Johnson-Maynard, Jodi L., Joschko, Monika, Kaneko, Nobuhiro, Kanianska, Radoslava, Keith, Aidan M., Kernecker, Maria L., Koné, Armand W., Kooch, Yahya, Kukkonen, Sanna T., Lalthanzara, H., Lammel, Daniel R., Lebedev, Iurii M., Le Cadre, Edith, Lincoln, Noa K., López-Hernández, Danilo, Loss, Scott R., Marichal, Raphael, Matula, Radim, Minamiya, Yukio, Moos, Jan Hendrik, Moreno, Gerardo, Morón-Ríos, Alejandro, Motohiro, Hasegawa, Muys, Bart, Neirynck, Johan, Norgrove, Lindsey, Novo, Marta, Nuutinen, Visa, Nuzzo, Victoria, Mujeeb Rahman, P., Pansu, Johan, Paudel, Shishir, Pérès, Guénola, Pérez-Camacho, Lorenzo, Ponge, Jean-François, Prietzel, Jörg, Rapoport, Irina B., Rashid, Muhammad Imtiaz, Rebollo, Salvador, Rodríguez, Miguel Á., Roth, Alexander M., Rousseau, Guillaume X., Rozen, Anna, Sayad, Ehsan, van Schaik, Loes, Scharenbroch, Bryant, Schirrmann, Michael, Schmidt, Olaf, Schröder, Boris, Seeber, Julia, Shashkov, Maxim P., Singh, Jaswinder, Smith, Sandy M., Steinwandter, Michael, Szlavecz, Katalin, Talavera, José Antonio, Trigo, Dolores, Tsukamoto, Jiro, Uribe-López, Sheila, de Valença, Anne W., Virto, Iñigo, Wackett, Adrian A., Warren, Matthew W., Webster, Emily R., Wehr, Nathaniel H., Whalen, Joann K., Wironen, Michael B., Wolters, Volkmar, Wu, Pengfei, Zenkova, Irina V., Zhang, Weixin, Cameron, Erin K., and Eisenhauer, Nico

Published
2021
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36. Clinical benefit of remdesivir in rhesus macaques infected with SARS-CoV-2

Author

Williamson, Brandi N., Feldmann, Friederike, Schwarz, Benjamin, Meade-White, Kimberly, Porter, Danielle P., Schulz, Jonathan, and van Doremalen, Neeltje

Subjects
Rhesus monkey -- Diseases -- Drug therapy, Environmental issues, Science and technology, Zoology and wildlife conservation
Abstract

Effective therapies to treat coronavirus disease 2019 (COVID-19) are urgently needed. While many investigational, approved, and repurposed drugs have been suggested as potential treatments, preclinical data from animal models can guide the search for effective treatments by ruling out those that lack efficacy in vivo. Remdesivir (GS-5734) is a nucleotide analogue prodrug with broad antiviral activity.sup.1,2 that is currently being investigated in COVID-19 clinical trials and recently received Emergency Use Authorization from the US Food and Drug Administration.sup.3,4. In animal models, remdesivir was effective against infection with Middle East respiratory syndrome coronavirus (MERS-CoV) and severe acute respiratory syndrome coronavirus (SARS-CoV).sup.2,5,6. In vitro, remdesivir inhibited replication of SARS-CoV-2.sup.7,8. Here we investigate the efficacy of remdesivir in a rhesus macaque model of SARS-CoV-2 infection.sup.9. Unlike vehicle-treated animals, macaques treated with remdesivir did not show signs of respiratory disease; they also showed reduced pulmonary infiltrates on radiographs and reduced virus titres in bronchoalveolar lavages twelve hours after the first dose. Virus shedding from the upper respiratory tract was not reduced by remdesivir treatment. At necropsy, remdesivir-treated animals had lower lung viral loads and reduced lung damage. Thus, treatment with remdesivir initiated early during infection had a clinical benefit in rhesus macaques infected with SARS-CoV-2. Although the rhesus macaque model does not represent the severe disease observed in some patients with COVID-19, our data support the early initiation of remdesivir treatment in patients with COVID-19 to prevent progression to pneumonia. The nucleotide analogue prodrug remdesivir reduces viral load and lung disease in a rhesus macaque model of SARS-CoV-2 infection., Author(s): Brandi N. Williamson [sup.1] , Friederike Feldmann [sup.2] , Benjamin Schwarz [sup.3] , Kimberly Meade-White [sup.1] , Danielle P. Porter [sup.4] , Jonathan Schulz [sup.1] , Neeltje van Doremalen [...]

Published
2020
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37. Branching laws for small unitary representations of GL(n,C)

Author

Möllers, Jan and Schwarz, Benjamin

Subjects
Mathematics - Representation Theory, Primary 22E45, Secondary 43A85
Abstract

The unitary principal series representations of $G=GL(n,\mathbb{C})$ induced from a character of the maximal parabolic subgroup $P=(GL(1,\mathbb{C})\times GL(n-1,\mathbb{C}))\ltimes\mathbb{C}^{n-1}$ attain the minimal Gelfand--Kirillov dimension among all infinite-dimensional unitary representations of $G$. We find the explicit branching laws for the restriction of these representations to symmetric subgroups of $G$., Comment: 14 pages

Published
2013
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38. Existence of nearly holomorphic sections on compact Hermitian symmetric spaces

Author

Schwarz, Benjamin

Subjects
Mathematics - Complex Variables, Mathematics - Representation Theory, 32M15 (Primary) 32D15, 22E46, 32A50, 32L10, 17C50 (Secondary)
Abstract

Let $X=U/K$ be a compact Hermitian symmetric space, and let $\sE$ be a $U$-homogeneous Hermitian vector bundle on $X$. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in $L^2(X,\sE)$ provided that non-trivial nearly holomorphic sections do exist. Here we investigate the problem of extending local nearly holomorphic sections to global ones and prove the existence of non-trivial nearly holomorphic sections. This extends the results on the $U$-type decomposition of $L^2(X,\sE)$ from our previous paper., Comment: 20 pages

Published
2013

39. Inequalities for generalized minors

Author

Schwarz, Benjamin

Subjects
Mathematics - Rings and Algebras, 15A45 (Primary) 17C50, 15A18 (Secondary)
Abstract

It is a classical result that the absolute value of any $k$-minor of an $r\times s$ real or complex matrix is bounded by the product of its first $k$ singular values. We generalize this statement to the context of real or complex simple Jordan pairs with generalized minors given by Jordan algebra determinants., Comment: 10 pages

Published
2013

40. Inducible histone K-to-M mutations are dynamic tools to probe the physiological role of site-specific histone methylation in vitro and in vivo

Author

Brumbaugh, Justin, Kim, Ik Soo, Ji, Fei, Huebner, Aaron J., Di Stefano, Bruno, Schwarz, Benjamin A., Charlton, Jocelyn, Coffey, Amy, Choi, Jiho, Walsh, Ryan M., Schindler, Jeffrey W., Anselmo, Anthony, Meissner, Alexander, Sadreyev, Ruslan I., Bernstein, Bradley E., Hock, Hanno, and Hochedlinger, Konrad

Published
2019
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41. Structure of the degenerate principal series on symmetric R-spaces and small representations

Author

Möllers, Jan and Schwarz, Benjamin

Subjects
Mathematics - Representation Theory
Abstract

Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whose nilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We study the degenerate principal series representations of $G$ on $C^\infty(X)$ in the case where $P$ is not conjugate to its opposite parabolic. We find the points of reducibility, the composition series and all unitarizable constituents. Among the unitarizable constituents we identify some small representations having as associated variety the minimal nilpotent $K_{\mathbb{C}}$-orbit in $\mathfrak{p}_{\mathbb{C}}^*$, where $K_{\mathbb{C}}$ is the complexification of a maximal compact subgroup $K\subseteq G$ and $\mathfrak{g}=\mathfrak{k}+\mathfrak{p}$ the corresponding Cartan decomposition., Comment: 29 pages, added Lemma 2.2 which fills a gap in the proof of Corollary 2.3

Published
2012
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44. Fractionated satellites : a systems engineering analysis

Author

Schwarz, Benjamin Samuel and Tatnall, Adrian

Subjects
629.47, TL Motor vehicles. Aeronautics. Astronautics
Abstract

The current method of operating space-based assets involves the design and launch of large, monolithic spacecraft. These spacecraft are not responsive to failures or changes in mission requirements, as both require the launch of a completely new spacecraft. The concept of fractionated spacecraft was introduced in 2006 by the US Defence Advanced Research Projects Agency (DARPA) as a way of designing and operating space systems which is more responsive than current methods. The fractionated concept involves the decomposition of the traditional monolithic satellite into a number of free-flying spacecraft connected wirelessly. The free-flying satellites each carry a subset of the required subsystems and share their fractionated resources to achieve the mission objectives. Since 2006, studies of this concept have focused on analyses of the value and utility provided by fractionated spacecraft or on design studies of specific systems. This thesis addresses two key questions: Firstly, is fractionation a mission enabling technology? Secondly, can design rules and guidelines be developed for fractionated satellites to allow continuity of measurements to be maintained and launched mass minimised? The first question is addressed by studying a payload and system for measuring coastal salinity from space. This provides an initial opportunity to assess the fractionated concept from a systems engineering point of view. The second question is addressed by undertaking a more general analysis of fractionated architectures, building on the knowledge gained in development of the fractionated coastal salinity measurement system. A computer model was developed to simulate the lifetime of different fractionated architectures when subjected to subsystem failures. A local search algorithm was used to find fractionated architectures which gave the best compromise between mass launched versus the operational time over a 50 year lifetime. The results from the application of this model showed that architectures that are highly fractionated, containing several homogeneous satellites, best achieved this compromise. These findings provide a contrast to the heterogeneously fractionated architectures proposed by DARPA. When a fractionated architecture is first implemented, the technology required to fractionate all the spacecraft subsystems may not be available. Consequently, the key to the implementation of these first fractionated architectures will be to ensure that there is redundancy in the fractionated subsystems spread across the architecture.

Published
2014

45. Nearly holomorphic sections on compact Hermitian symmetric spaces

Author

Schwarz, Benjamin

Subjects
Mathematics - Representation Theory, Mathematics - Complex Variables, 32A50 (Primary) 22E46, 32M15, 32L10, 17C50 (Secondary)
Abstract

Let X be a K\"ahler manifold, and E be a Hermitian vector bundle on X. We investigate the space N(X,E) of nearly holomorphic sections in E, which generalizes the notion of nearly holomorphic functions introduced by Shimura. If X=U/K is a compact Hermitian symmetric space, and E is U-homogeneous, it turns out that N(X,E) coincides with the space of $U$-finite vectors in C^\infty(X,E), and we obtain new results on the U-type decomposition of the Hilbert space of square integrable sections. As an application, we determine this decomposition for the holomorphic tangent space of X., Comment: 34 pages

Published
2012

46. Symplectic branching laws and Hermitian symmetric spaces

Author

Schwarz, Benjamin and Seppänen, Henrik

Subjects
Mathematics - Representation Theory, Mathematics - Complex Variables, Mathematics - Symplectic Geometry, 22E46, 53D20, 17C50, 32M15, 32L05
Abstract

Let $G$ be a complex simple Lie group, and let $U \subseteq G$ be a maximal compact subgroup. Assume that $G$ admits a homogenous space $X=G/Q=U/K$ which is a compact Hermitian symmetric space. Let $\mathscr{L} \rightarrow X$ be the ample line bundle which generates the Picard group of $X$. In this paper we study the restrictions to $K$ of the family $(H^0(X, \mathscr{L}^k))_{k \in \N}$ of irreducible $G$-representations. We describe explicitly the moment polytopes for the moment maps $X \rightarrow \fk^*$ associated to positive integer multiples of the Kostant-Kirillov symplectic form on $X$, and we use these, together with an explicit characterization of the closed $K^\C$-orbits on $X$, to find the decompositions of the spaces $H^0(X,\mathscr{L}^k)$. We also construct a natural Okounkov body for $\mathscr{L}$ and the $K$-action, and identify it with the smallest of the moment polytopes above. In particular, the Okounkov body is a convex polytope. In fact, we even prove the stronger property that the semigroup defining the Okounkov body is finitely generated.

Published
2011

50. How Britain Became Civilized

Author

Schwarz, Benjamin

Subjects
High Minds: The Victorians and the Birth of Modern Britain (Nonfiction work) -- Heffer, Simon, Books -- Book reviews, Literature/writing
Abstract

HIGH MINDSThe Victorians and the Birth of Modern BritainBy Simon Heffer Writing during World War II, George Orwell remarked upon the contrast between the ''gentleness'' that characterized contemporary English civilization [...]

Published
2022

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