Weyl modules and Levi subalgebras

TL;DR

This paper investigates how Weyl modules for simple Lie algebras behave when restricted to Levi subalgebras, providing conditions for when these restrictions remain Weyl modules.

Contribution

It identifies necessary and sufficient conditions for the restriction of Weyl modules to Levi subalgebras to preserve their Weyl module structure.

Findings

Criteria for restriction to yield Weyl modules

Characterization of global and local Weyl module restrictions

Insights into module structure under Levi subalgebra restriction

Abstract

For a simple complex Lie algebra of finite rank and classical type, we fix a triangular decomposition and consider the simple Levi subalgebras associated to closed subsets of roots. We study the restriction of global and local Weyl modules of current algebras to this Levi subalgebra. We identify necessary and sufficient conditions on a pair of a Levi subalgebra and a dominant integral weight, such that the restricted module is a global (resp. a local) Weyl module.