A Twining Character Formula For Demazure Modules

Abstract

We prove a formula for the twining characters of certain Demazure modules, over a Borel subalgebra b of a finite dimensional complex semisimple Lie algebra g. This formula describes the twining character of the Demazure module by the ω-Demazure operator associated to an element of the Weyl group that is fixed by the Dynkin diagram automorphism ω of g. Our result is a refinement of the twining character formula for the irreducible highest weight g-modules of symmetric dominant integral highest weights, and also of the ordinary Demazure character formula.