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

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概要

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• For a Weyl group $W$ of a classical root system $(Σ, E)$, 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.

• 東京大学の論文

著者

• Oshima Toshio

  Department Of Mathematical Sciences University Of Tokyo

• Oshima Toshio

  Department Of Chemical Engineering Faculty Of Engineering Himeji Institute Of Technology

• Sekiguchi Hideko

  Department of Mathematical Sciences, University of Tokyo

• Sekiguchi Hideko

  Department Of Mathematical Sciences University Of Tokyo

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