1. Filtering cohomology of ordinary and Lagrangian Grassmannians
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"q-binomials, The 2020 Polymath Jr. REU, group", the Grassmannian, Ahmed, Huda, Chishti, Rasiel, Chiu, Yu-Cheng, Dorpalen-Barry, Galen, Ellis, Jeremy, Fang, David, Feigen, Michael, Feigert, Jonathan, González, Mabel, Harker, Dylan, Wei, Jiaye, Joshi, Bhavna, Kulkarni, Gandhar, Lad, Kapil, Liu, Zhen, Mingyang, Ma, Myers, Lance, Nigam, Arjun, Popescu, Tudor, Reiner, Victor, Rong, Zijian, Sukarto, Eunice, Villamil, Leonardo Mendez, Wang, Chuanyi, Wang, Napoleon, Yamin, Ajmain, Yu, Jeffery, Yu, Matthew, Zhang, Yuanning, Zhu, Ziye, and Zijian, Chen
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Mathematics - Combinatorics ,05E14, 05E05, 14N15 - Abstract
This paper studies, for a positive integer $m$, the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most $m$. We build in two ways upon a conjecture for the Hilbert series of this subalgebra due to Reiner and Tudose. The first reinterprets it in terms of the operation of $k$-conjugation, suggesting two conjectural bases for the subalgebras that would imply their conjecture. The second introduces an analogous conjecture for the cohomology of Lagrangian Grassmannians., Comment: Version to appear in Involve
- Published
- 2020
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