Finite-dimensional representations of twisted hyper loop algebras

TL;DR

This paper classifies finite-dimensional representations of twisted hyper loop algebras, introduces universal Weyl modules, and relates their simple modules to those of non-twisted hyper loop algebras under certain conditions.

Contribution

It provides a classification of irreducible modules, defines universal Weyl modules, and establishes an isomorphism between twisted and non-twisted hyper loop algebra modules.

Findings

Classification of irreducible modules

Definition of universal Weyl modules

Isomorphism between twisted and non-twisted modules under certain conditions

Abstract

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the classification of the irreducible modules, the definition of the universal highest-weight modules, called the Weyl modules, and, under a certain mild restriction on the characteristic of the ground field, a proof that the simple modules and the Weyl modules for the twisted hyper loop algebras are isomorphic to appropriate simple and Weyl modules for the non-twisted hyper loop algebras, respectively, via restriction of the action.