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Lattice polytopes, Hecke operators, and the Ehrhart polynomial

Paul E. Gunnells·Fernando Rodriguez Villegas
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Abstract

Let P be a simple lattice polytope. We define an action of the Hecke operators on E (P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E (P). We also describe how the Brion-Vergne formula transforms under the Hecke operators for nonsingular lattice polytopes P.

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Paul E. Gunnells, Fernando Rodriguez Villegas. 2004-05-29. Lattice polytopes, Hecke operators, and the Ehrhart polynomial. https://arxiv.org/abs/math/0405573

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