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

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

2009-05-27

arxiv.org/abs/0905.4533v1

Mathematics

Representation Theory

12 pages

Scientific paper

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.

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