Lattice polytopes, Hecke operators, and the Ehrhart polynomial

PE Gunnells, University of Massachusetts - Amherst
FR Villegas

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This is the pre-published version harvested from ArXiv. The published version is located at http://www.springerlink.com/content/qr18k61r4j132654/

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 for E(P) transforms under the Hecke operators for nonsingular lattice polytopes P.