Permutation representations on Schubert varieties

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dc.creatorTymoczko, Julianna S.
dc.date2006-04-26
dc.date2007-06-04
dc.date.accessioned2026-07-07T08:07:44Z
dc.date.available2026-07-07T08:07:44Z
dc.descriptionThis paper defines and studies permutation representations on the equivariant cohomology of Schubert varieties, as representations both over C and over C[t_1, t_2,...,t_n]. We show these group actions are the same as an action of simple transpositions studied geometrically by M. Brion, and give topological meaning to the divided difference operators studied by Berstein-Gelfand-Gelfand, Demazure, Kostant-Kumar, and others. We analyze these representations using the combinatorial approach to equivariant cohomology introduced by Goresky-Kottwitz-MacPherson. We find that each permutation representation on equivariant cohomology produces a representation on ordinary cohomology that is trivial, though the equivariant representation is not.
dc.description20 pages, v2: minor revisions
dc.identifierhttps://arxiv.org/abs/math/0604578
dc.identifierhttp://arxiv.org/abs/math/0604578
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131034
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject20C30; 05E10, 14M15,55N91, 20F55
dc.titlePermutation representations on Schubert varieties
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