MR2177118
Suzuki, Takao
Takao SUZUKI
Affine Weyl Group Symmetry of the Garnier System
Funkcialaj Ekvacioj. Serio Internacia
48
2005
203--230
http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-2/48_203.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2177118
In this paper, we show that the Garnier system in $n$-variables has affine Weyl group symmetry of type $B_{n+3}^{(1)}$. 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.
Affine Weyl group, Bäcklund transformations, Garnier system, Schlesinger system, $\tau$-functions.
33E17, 20F55, 37K35.
48-203
2005
Affine Weyl Group Symmetry of the Garnier System
SUZUKI, Takao
Takao SUZUKI
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