Affine Weyl group symmetry of the Garnier system
Abstract
We show that the Garnier system in n-variables has affine Weyl group symmetry of type B(1)n+3. We also formulate the τ functions for the Garnier system (or the Schlesinger system of rank 2) on the root lattice Q(Cn+3) and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear differential equations.
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