# Demazure and local Weyl modules for twisted hyper current algebras

## TL;DR

This paper establishes an isomorphism between local graded Weyl modules and level 1 Demazure modules for twisted hypercurrent algebras, linking twisted and untwisted cases in the representation theory of hypercurrent algebras.

## Contribution

It proves that local graded Weyl modules for twisted hypercurrent algebras are isomorphic to level 1 Demazure modules and are restrictions of untwisted modules, revealing structural connections.

## Key findings

- Local graded Weyl modules are isomorphic to level 1 Demazure modules.
- These modules are restrictions of untwisted hypercurrent algebra modules.
- The results unify twisted and untwisted hypercurrent algebra representations.

## Abstract

In this paper, we study local graded Weyl modules and Demazure modules for twisted hypercurrent algebras. We prove that local graded Weyl modules for a twisted hypercurrent algebra are isomorphic to the corresponding level 1 Demazure modules, and moreover, that they are restrictions of corresponding local graded Weyl modules for the untwisted hypercurrent algebra.