## Abstract

We give a birational realization of affine Weyl group of type A^{(1)}_{m-1} × A^{(1)}_{n-1}. We apply this representation to construct some discrete integrable systems and discrete Painlevé equations. Our construction has a combinatorial counterpart through the ultra-discretization procedure.

Original language | English |
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Pages (from-to) | 211-219 |

Number of pages | 9 |

Journal | Letters in Mathematical Physics |

Volume | 60 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 2002 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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