On Demazure and local Weyl modules for affine hyperalgebras

TL;DR

This paper proves that graded local Weyl modules for hyper current algebras in positive characteristic have Demazure flags, and in simply laced cases, are isomorphic to Demazure modules, extending known results from characteristic zero.

Contribution

It establishes Demazure flags for local Weyl modules in positive characteristic and shows their independence from the ground field, extending prior characteristic zero results.

Findings

Demazure flags exist for graded local Weyl modules in positive characteristic.

In simply laced cases, local Weyl modules are isomorphic to Demazure modules.

Character of local Weyl modules depends only on highest weight, not on the ground field.

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, i.e., the graded local Weyl modules are isomorphic to Demazure modules. This extends to the positive characteristic setting results of Fourier-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.