Demazure modules and Weyl modules: The twisted current case

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.

26 pages

References in corpus (2)

• Irreducible finite-dimensional representations of equivariant map algebras
• Local Weyl modules for equivariant map algebras with free abelian group actions

Cited by in corpus (9)

• BGG reciprocity for current algebras
• Fusion products and toroidal algebras
• Weyl modules for the hyperspecial current algebra
• Twisted Demazure modules, fusion product decomposition and twisted Q--systems
• Twisted zastava and $q$-Whittaker functions
• On Demazure and local Weyl modules for affine hyperalgebras
• Finite-dimensional representations of twisted hyper loop algebras
• Beilinson-Drinfeld Schubert varieties of parahoric group schemes and twisted global Demazure modules
• Demazure and local Weyl modules for twisted hyper current algebras