Projective reduction of the discrete Painlevé system of type $(A_2+A_1)^{(1)}$

Details Projective reduction of the discrete Painlevé system of type $(A_2+A_1)^{(1)}$ Projective reduction of the discrete Painlevé system of type $(A_2+A_1)^{(1)}$

2009-10-23

arxiv.org/abs/0910.4439v6

International Mathematics Research Notices, (2010)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, 10 figures

Scientific paper

10.1093/imrn/rnq089

We consider the q-Painlev\'e III equation arising from the birational representation of the affine Weyl group of type $(A_2 + A_1)^{(1)}$. We study the reduction of the q-Painlev\'e III equation to the q-Painlev\'e II equation from the viewpoint of affine Weyl group symmetry. In particular, the mechanism of apparent inconsistency between the hypergeometric solutions to both equations is clarified by using factorization of difference operators and the $\tau$ functions.

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