Robin Langer, Michael J. Schlosser, S. Ole Warnaar, “Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture”, SIGMA, 2009, Volume 5,055, 20 pp.

This article is cited in 7 papers

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

Robin Langer^a, Michael J. Schlosser^b, S. Ole Warnaar^c

^a Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
^b Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Vienna, Austria
^c School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia

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.

Keywords: theta functions; Macdonald polynomials; elliptic hypergeometric series.

MSC: 05E05; 33D52; 33D67

Received: March 1, 2009; in final form May 19, 2009; Published online May 25, 2009

Language: English

DOI: 10.3842/SIGMA.2009.055