Generalized Weyl modules and nonsymmetric $q$-Whittaker functions

TL;DR

This paper introduces generalized global Weyl modules and connects their graded characters to nonsymmetric Macdonald polynomials and $q$-Whittaker functions, revealing new algebraic and combinatorial relationships.

Contribution

It establishes a novel link between generalized Weyl modules and nonsymmetric $q$-Whittaker functions, expanding understanding of their algebraic structure.

Findings

The series part of the nonsymmetric $q$-Whittaker function generates graded characters of generalized global Weyl modules.

A new relationship between Weyl modules and nonsymmetric Macdonald polynomials is demonstrated.

The work provides a framework for further exploration of nonsymmetric special functions in representation theory.

Abstract

We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker function is a generating function for the graded characters of generalized global Weyl modules.