Demazure slices of type $A_{2l}^{(2)}$

TL;DR

This paper studies Demazure slices of type $A_{2l}^{(2)}$, showing their relation to global Weyl modules, computing extensions, and connecting graded characters to nonsymmetric Macdonald-Koornwinder polynomials.

Contribution

It demonstrates that global Weyl modules are filtered by Demazure slices and establishes a link between Demazure slices and nonsymmetric Macdonald-Koornwinder polynomials.

Findings

Global Weyl modules are filtered by Demazure slices.

Graded characters of Demazure slices equal nonsymmetric Macdonald-Koornwinder polynomials divided by their norm.

Global Weyl modules are free over their endomorphism ring.

Abstract

We consider a Demazure slice of type $A_{2l}^{(2)}$, that is an associated graded piece of an infinite-dimensional version of a Demazure module. We show that a global Weyl module of a hyperspecial current algebra of type $A_{2l}^{(2)}$ is filtered by Demazure slices. We calculate extensions between a Demazure slice and a usual Demazure module and prove that a graded character of a Demazure slice is equal to a nonsymmetric Macdonald-Koornwinder polynomial divided by its norm. In the last section, we prove that a global Weyl module of the special current algebra of type $A_{2l}^{(2)}$ is a free module over the polynomial ring arising as the endomorphism ring of itself.