Affine Hall-Littlewood functions for A₁⁽¹⁾ and some constant term identities of Cherednik-Macdonald-Mehta type

2009/05/27 by Sankaran Viswanath, Viswanath, Sankaran
Mathematics · #17B67 #33D67 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B67 #msc:33D67

paper · pdf · doi:10.48550/arxiv.0905.4533

12 pages

arxiv created 2009/05/27 · openalex publication_date 2009/05/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A₁⁽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.

Citations

• A new take on spherical, Whittaker and Bessel functions (Spherical and Whittaker functions via DAHA I,II)
• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

Related

• The t-analog of the basic string function for twisted affine Kac-Moody algebras
• The t-analogs of string functions for A₁⁽¹⁾ and Hecke indefinite modular forms
• On string functions of the generalized parafermionic theories, mock theta functions, and false theta functions, II
• Affine Jacobi-Trudi formulas and q,t-Rogers-Ramanujan identities
• Characters of representations of affine Kac-Moody Lie algebras at the critical level