Demazure modules and Weyl modules: the twisted current case (Q2849040)

This work contributes to the ongoing study of finite-dimensional representations of various extensions of simple complex Lie algebras \(\mathfrak{g}\). These extensions include current algebras \(\mathfrak{g} \otimes \mathbb{C}[t]\) and loop algebras \(\mathfrak{g} \otimes \mathbb{C}[t,t^{-1}]\), as well as versions of these twisted by taking fixed points of the action of Dynkin diagram automorphisms. Unlike the classical semisimple situation, the theory is difficult and proceeds by examining particular classes of modules, with a view to obtaining dimension and character formulae.NEWLINENEWLINEThe present paper examines graded twisted Weyl modules, showing that these are isomorphic to level one Demazure modules for the twisted affine Kac-Moody algebra and also that, in the majority of cases, they may be obtained as associated graded modules of Weyl modules for the corresponding untwisted loop algebra. These results allow the transfer of known results from the untwisted setting to the twisted one, yielding the sought dimension and character formulae.