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

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.