Discrete dynamical systems with W(A(1)m-1 × A(1)n-1) symmetry
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 Painlev\'e equations. Our construction has a combinatorial counterpart through the ultra-discretization procedure.
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