Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture

Abstract

We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable, basic case.

References in corpus (3)

• Summation and transformation formulas for elliptic hypergeometric series
• Inversion of the Pieri formula for Macdonald polynomials
• On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series

Cited by in corpus (12)

• Multivariate Quadratic Transformations and the Interpolation Kernel
• An elliptic hypergeometric integral with W(F_4) symmetry
• Elliptic Littlewood identities
• Elliptic hypergeometric functions associated with root systems
• An (inverse) Pieri formula for Macdonald polynomials of type C
• Higher order deformed elliptic Ruijsenaars operators
• Skew RSK dynamics: Greene invariants, affine crystals and applications to $q$-Whittaker polynomials
• Wall-crossing for vortex partition function and handsaw quiver varierty
• Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$
• (q,t)-hook formula for Birds and Banners
• Macdonald polynomials and symmetric functions
• $K$-theoretic wall-crossing formulas and multiple basic hypergeometric series