Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 035, 30 pages      arXiv:0903.4102      http://dx.doi.org/10.3842/SIGMA.2009.035
Contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions”

Hypergeometric τ-Functions of the q-Painlevé System of Type E7(1)

Tetsu Masuda
Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa, 229-8558, Japan

Received November 27, 2008, in final form March 10, 2009; Published online March 24, 2009

Abstract
We present the τ-functions for the hypergeometric solutions to the q-Painlevé system of type E7(1) in a determinant formula whose entries are given by the basic hypergeometric function 8W7. By using the W(D5) symmetry of the function 8W7, we construct a set of twelve solutions and describe the action of  ~W(D6(1)) on the set.

Key words: q-Painlevé system; q-hypergeometric function; Weyl group; τ-function.

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