Equivariant Ehrhart theory |
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Authors: | Alan Stapledon |
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Institution: | Department of Mathematics, University of British Columbia, BC, Canada V6T 1Z2 |
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Abstract: | 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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Keywords: | Lattice polytopes Toric varieties Group actions on varieties |
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