## Commuting families of differential operators invariant under the action of a Weyl group

J. Math. Sci. Univ. Tokyo
Vol. 2 (1995), No. 1, Page 1--75.

Oshima, Toshio ; Sekiguchi, Hideko
Commuting families of differential operators invariant under the action of a Weyl group
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Abstract:
For a Weyl group $W$ of a classical root system $(Î£, E)$, we study $W$-invariant commuting differential operators on $E$ whose highest order terms generate the $W$-invariant differential operators with constant coefficients. We show that the potential function for the Laplacian in this commuting family of differential operators is expressed by the Weierstrass elliptic functions. The commuting differential operators define a generalization of hypergeometric equations.

Mathematics Subject Classification (1991): Primary 58F07; Secondary 35Q58, 33E30, 34K05
Mathematical Reviews Number: MR1348022