The t-analog of the basic string function for twisted affine Kac-Moody algebras

TL;DR

This paper derives a closed-form expression for the t-analog of the basic string function in twisted affine Kac-Moody algebras, extending previous results for untwisted cases using constant term identities.

Contribution

It provides an explicit formula for the t-string function in twisted affine Kac-Moody algebras, incorporating generalized exponents and extending prior untwisted algebra results.

Findings

Explicit closed-form expression for t-string function

Uses constant term identities of Macdonald and Cherednik

Extends previous work to twisted affine algebras

Abstract

We study Lusztig's t-analog of weight multiplicities associated to level one representations of twisted affine Kac-Moody algebras. An explicit closed form expression is obtained for the corresponding t-string function using constant term identities of Macdonald and Cherednik. The closed form involves the generalized exponents of the graded pieces of the twisted affine algebra, considered as modules for the underlying finite dimensional simple Lie algebra. This extends previous work on level 1 t-string functions for the untwisted simply-laced affine Kac-Moody algebras.