### Abstract

We consider the q-Painlevé 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-Painlevé III equation to the q-Painlevé 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.

Original language | English |
---|---|

Pages (from-to) | 930-966 |

Number of pages | 37 |

Journal | International Mathematics Research Notices |

Volume | 2011 |

Issue number | 4 |

DOIs | |

Publication status | Published - Mar 7 2011 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

_{2}+ A

_{1})

^{(1)}.

*International Mathematics Research Notices*,

*2011*(4), 930-966. https://doi.org/10.1093/imrn/rnq089

**Projective reduction of the discrete painlevé system of type (A _{2} + A_{1})^{(1)}.** / Kajiwara, Kenji; Nakazono, Nobutaka; Tsuda, Teruhisa.

Research output: Contribution to journal › Article

_{2}+ A

_{1})

^{(1)}',

*International Mathematics Research Notices*, vol. 2011, no. 4, pp. 930-966. https://doi.org/10.1093/imrn/rnq089

_{2}+ A

_{1})

^{(1)}. International Mathematics Research Notices. 2011 Mar 7;2011(4):930-966. https://doi.org/10.1093/imrn/rnq089

}

TY - JOUR

T1 - Projective reduction of the discrete painlevé system of type (A 2 + A1)(1)

AU - Kajiwara, Kenji

AU - Nakazono, Nobutaka

AU - Tsuda, Teruhisa

PY - 2011/3/7

Y1 - 2011/3/7

N2 - We consider the q-Painlevé III equation arising from the birational representation of the affine Weyl group of type (A2 + A 1)(1). We study the reduction of the q-Painlevé III equation to the q-Painlevé 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.

AB - We consider the q-Painlevé III equation arising from the birational representation of the affine Weyl group of type (A2 + A 1)(1). We study the reduction of the q-Painlevé III equation to the q-Painlevé 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.

UR - http://www.scopus.com/inward/record.url?scp=79952173534&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952173534&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnq089

DO - 10.1093/imrn/rnq089

M3 - Article

AN - SCOPUS:79952173534

VL - 2011

SP - 930

EP - 966

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 4

ER -