Hypergeometric theta functions and elliptic Macdonald polynomials

Abstract

Elliptic Macdonald polynomials of sl(2)-type and level 2 are introduced. Suitable limits of elliptic Macdonald polynomials are the standard Macdonald polynomials and conformal blocks. Identities for elliptic Macdonald polynomials, in particular their modular properties, are studied.

16 pages, reference added

References in corpus (2)

• The elliptic gamma function and SL(3,Z) x Z^3
• q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)

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• The deformed Inozemtsev spin chain
• Traces of intertwiners for quantum affine sl_2 and Felder-Varchenko functions
• Affine Macdonald conjectures and special values of Felder-Varchenko functions
• Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials