Representations of hypersurfaces and equivariant Ehrhart theory

We give an explicit description of the representations of a finite group acting on the cohomology of a `general' invariant hypersurface in a toric variety. We show how this naturally leads to an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes, and prove several equivariant versions of classical results. As an example, we show how the representations of a Weyl group acting on the cohomology of the toric variety associated to a root system naturally appear.

After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

Anthony Henderson [email protected].