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

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

2001-06-19

arxiv.org/abs/nlin/0106029v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages

Scientific paper

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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