Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator

2002/03/06 by G. Felder, Giovanni Felder, L. Stevens +5
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0203049

Latex, 19 pages; added remark in section 2 and remark in section 6, added references

openalex publication_date 2002/03/06 · arxiv created 2002/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the space of elliptic hypergeometric functions of the sl₂ type associated with elliptic curves with one marked point. This space represents conformal blocks in the sl₂ WZW model of CFT. The modular group acts on this space. We give formulas for the matrices of the action in terms of values at roots of unity of Macdonald polynomials of the sl₂ type.

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