Affine Hall-Littlewood functions for $A_1^{(1)}$ and some constant term identities of Cherednik-Macdonald-Mehta type

TL;DR

This paper derives explicit formulas for t-analogs of string functions in affine Kac-Moody algebra A_1^{(1)} and uses them to establish new identities related to affine Hall-Littlewood functions and generalizations of Macdonald-Mehta identities.

Contribution

It provides closed-form formulas for specific t-string functions and introduces higher-level generalizations of key constant term identities.

Findings

Explicit formulas for t-string functions at levels 2 and 4

New identities for affine Hall-Littlewood functions

Generalizations of Macdonald-Mehta constant term identities

Abstract

We study $t$-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra $A_1^{(1)}$. We obtain closed form formulas for certain $t$-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher-level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.