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Your search keyword '"symmetric automorphism"' showing total 2 results
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2 results on '"symmetric automorphism"'

1. Multivector and Extensor Calculus

Author

Rodrigues, Waldyr A., Jr, Capelas de Oliveira, Edmundo, Bartelmann, Matthias, Series editor, Englert, Berthold-Georg, Series editor, Hänggi, Peter, Series editor, Hjorth-Jensen, Morten, Series editor, Jones, Richard A L, Series editor, Lewenstein, Maciej, Series editor, von Löhneysen, H., Series editor, Raimond, Jean-Michel, Series editor, Rubio, Angel, Series editor, Theisen, Stefan, Series editor, Vollhardt, Prof. Dieter, Series editor, Wells, James, Series editor, Zank, Gary P., Series editor, Salmhofer, Manfred, Series editor, Rodrigues, Jr, Waldyr A., and Capelas de Oliveira, Edmundo

Published
2016
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2. Representation stability for the cohomology of the pure string motion groups

Author

Jennifer C. H. Wilson

Subjects
signed permutation group, Pure mathematics, basis-conjugating automorphism, circle-braid group, 20C15, string motion group, Motion (geometry), Characterization (mathematics), String (physics), High Energy Physics::Theory, Mathematics - Geometric Topology, symmetric automorphism, FOS: Mathematics, Algebraic Topology (math.AT), motion group, Mathematics - Algebraic Topology, Representation Theory (math.RT), hyperoctahedral group, Mathematics, representation stability, 20F28, Conjecture, Group (mathematics), homological stability, Geometric Topology (math.GT), Hyperoctahedral group, 20J06, Cohomology, Transfer (group theory), 57M25, Geometry and Topology, braid-permutation group, Mathematics - Representation Theory
Abstract

The cohomology of the pure string motion group PSigma_n admits a natural action by the hyperoctahedral group W_n. Church and Farb conjectured that for each k > 0, the sequence of degree k rational cohomology groups of PSigma_n is uniformly representation stable with respect to the induced action by W_n, that is, the description of the groups' decompositions into irreducible W_n representations stabilizes for n >> k. We use a characterization of the cohomology groups given by Jensen, McCammond, and Meier to prove this conjecture. Using a transfer argument, we further deduce that the rational cohomology groups of the string motion group vanish in positive degree. We also prove that the subgroup of orientation-preserving string motions, also known as the braid-permutation group, is rationally cohomologically stable in the classical sense., 24 pages, 3 figures

Published
2012

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