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

2009/05/25 by Robin Langer, Michael J. Schlosser, S. Ole Warnaar · 1 citation
Mathematics · #math.CA #math.CO

paper · pdf · doi:10.3842/sigma.2009.055

published as SIGMA 5 (2009), 055, 20 pages

arxiv created 2009/05/25 · arxiv updated 2009/12/01

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.

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