Rational points and Coxeter group actions on the cohomology of toric varieties

G I Lehrer

Abstract

We derive a simple formula for the action of a finite crystallographic Coxeter group on the cohomology of its associated complex toric variety, using the method of counting rational points over finite fields, and the Hodge structure of the cohomology. Various applications are given, including the determination of the graded multiplicity of the reflection representation.

AMS Subject Classification: Primary 14M25, 14F40; Secondary 14G05, 20G40, 14L30.