Equivariant Ehrhart theory

Details Equivariant Ehrhart theory Equivariant Ehrhart theory

2010-03-30

arxiv.org/abs/1003.5875v3

Mathematics

Combinatorics

40 pages. Final version. To appear in Adv. Math

Scientific paper

Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of numerous classical results, and give applications to the Ehrhart theory of rational polytopes and centrally symmetric polytopes. We also recover a character formula of Procesi, Dolgachev, Lunts and Stembridge for the action of a Weyl group on the cohomology of a toric variety associated to a root system.

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