On Demazure and local Weyl modules for affine hyperalgebras

Angelo Bianchi, Tiago Macedo and Adriano Moura

Vol. 274 (2015), No. 2, 257–303

DOI: 10.2140/pjm.2015.274.257

Abstract

We establish the existence of Demazure flags for graded local Weyl modules for hyper current algebras in positive characteristic. If the underlying simple Lie algebra is simply laced, the flag has length one; that is, the graded local Weyl modules are isomorphic to Demazure modules. This extends to the positive characteristic setting results of Chari and Loktev, Fourier and Littelmann, and Naoi for current algebras in characteristic zero. Using this result, we prove that the character of local Weyl modules for hyper loop algebras depend only on the highest weight, but not on the (algebraically closed) ground field, and deduce a tensor product factorization for them.

Keywords

Weyl modules, Demazure modules, hyperalgebras, affine Kac–Moody algebras, twisted affine algebras

Mathematical Subject Classification 2010

Primary: 17B10, 17B65

Secondary: 17B37, 20G42

Milestones

Received: 23 July 2013

Accepted: 14 September 2014

Published: 1 April 2015