Affine Weyl group symmetry of the Garnier system

Details Affine Weyl group symmetry of the Garnier system Affine Weyl group symmetry of the Garnier system

2003-12-25

arxiv.org/abs/math-ph/0312068v2

Physics

Mathematical Physics

33 pages

Scientific paper

We show that the Garnier system in n-variables has affine Weyl group symmetry
of type $B^{(1)}_{n+3}$. We also formulate the $\tau$ functions for the Garnier
system (or the Schlesinger system of rank 2) on the root lattice $Q(C_{n+3})$
and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear
differential equations.

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