Discrete dynamical systems with $W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})$ symmetry

Kenji Kajiwara; Masatoshi Noumi; Yasuhiko Yamada

arxiv: nlin/0106029 · v1 · submitted 2001-06-19 · 🌊 nlin.SI

Discrete dynamical systems with W(A⁽¹⁾_(m-1) times A⁽¹⁾_(n-1)) symmetry

Kenji Kajiwara , Masatoshi Noumi , Yasuhiko Yamada This is my paper

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keywords discretesystemstimesaffineapplybirationalcombinatorialconstruct

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

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Discrete dynamical systems with W(A⁽¹⁾_(m-1) times A⁽¹⁾_(n-1)) symmetry

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