Generalized Weyl modules for twisted current algebras

TL;DR

This paper introduces generalized Weyl modules for twisted current algebras, exploring their properties and connections to nonsymmetric Macdonald polynomials, and computes classical Weyl module dimensions in previously unknown cases.

Contribution

It presents the concept of generalized Weyl modules for twisted current algebras and links them to nonsymmetric Macdonald polynomials, advancing the understanding of their structure.

Findings

Established properties of generalized Weyl modules

Connected modules to nonsymmetric Macdonald polynomials

Computed dimensions of classical Weyl modules in new cases

Abstract

We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we compute the dimension of the classical Weyl modules in the remaining unknown case.