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

Kenji Kajiwara; Nobutaka Nakazono; Teruhisa Tsuda

doi:10.1093/imrn/rnq089

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

Kenji Kajiwara, Nobutaka Nakazono, Teruhisa Tsuda

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	930-966
Number of pages	37
Journal	International Mathematics Research Notices
Volume	2011
Issue number	4
DOIs	https://doi.org/10.1093/imrn/rnq089
Publication status	Published - 2011

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1093/imrn/rnq089

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abstract = "We consider the q-Painlev{\'e} 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-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 τ functions.",

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AU - Nakazono, Nobutaka

AU - Tsuda, Teruhisa

N1 - Funding Information: This work has been partially supported by the JSPS Grant-in-Aid for Scientific Research

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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.

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

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