Demazure modules and Weyl modules: The twisted current case

TL;DR

This paper establishes a correspondence between graded twisted Weyl modules and Demazure modules for twisted affine Kac-Moody algebras, providing new dimension and character formulas for twisted cases.

Contribution

It proves that twisted Weyl modules are isomorphic to Demazure modules and derives their dimension and character formulas, extending known results from untwisted to twisted types.

Findings

Graded twisted Weyl modules are isomorphic to level one Demazure modules.

Dimension and character formulas are obtained for twisted modules.

Twisted Weyl modules depend only on their classical highest weight.

Abstract

We study finite-dimensional respresentations of twisted current algebras and show that any graded twisted Weyl module is isomorphic to level one Demazure module for the twisted affine Kac-Moody algebra. Using the tensor product property of Demazure modules, we obtain, by analyzing the fundamental Weyl modules, dimension and character formulas. Moreover we prove that graded twisted Weyl modules can be obtained by taking the associated graded modules of Weyl modules for the loop algebra, which implies that its dimension and classical character are independent of the support and depend only on its classical highest weight. These results were known before for untwisted current algebras and are new for all twisted types.