## Quantization of differential systems with the affine Weyl group symmetries of type $C_N^{(1)}$

J. Math. Sci. Univ. Tokyo
Vol. 15 (2008), No. 4, Page 493--519.

Nagoya, Hajime
Quantization of differential systems with the affine Weyl group symmetries of type $C_N^{(1)}$
We construct systems of nonlinear differential equations with affine Weyl group symmetries of type $C_N^{(1)}$, as compatibility conditions of linear differential equations. These systems are Hamiltonian systems and those Hamiltonians are mutually commutative. We also construct a quantization of these systems with affine Weyl group symmetries of type $C_N^{(1)}$.