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

SIGMA 12 (2016), 051, 23 pages      arXiv:1601.05327      https://doi.org/10.3842/SIGMA.2016.051

Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1')^{(1)}$

Nobutaka Nakazono
School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia

Received February 01, 2016, in final form May 16, 2016; Published online May 20, 2016

Abstract
We consider $q$-Painlevé equations arising from birational representations of the extended affine Weyl groups of $A_4^{(1)}$- and $(A_1+A_1)^{(1)}$-types. We study their hypergeometric solutions on the level of $\tau$ functions.

Key words: $q$-Painlevé equation; basic hypergeometric function; affine Weyl group; $\tau$ function.

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