Projective Reduction of the Discrete Painlevé System of Type (A2 + A1)(1)

@article{Kajiwara2010ProjectiveRO,
  title={Projective Reduction of the Discrete Painlev{\'e} System of Type (A2 + A1)(1)},
  author={K. Kajiwara and Nobutaka Nakazono and Teruhisa Tsuda},
  journal={International Mathematics Research Notices},
  year={2010},
  volume={2011},
  pages={930-966}
}
We consider the q-Painleve 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-Painleve III equation to the q-Painleve 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 τ functions. 
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