Commuting families of differential operators invariant under the action of a Weyl group
Commuting families of differential operators invariant under the action of a Weyl group
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Weyl群作用下不变的微分算子通勤族
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
Hideko Sekiguchi
中科院分区：
文献类型：
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作者：
T. Oshima;Hideko Sekiguchi
对于经典根系（E，E）的Weyl群W，研究了E上W -不变的交换微分算子，其最高阶项生成W -不变的常系数微分算子.证明了这类可换微分算子族中拉普拉斯算子的势函数可用Weierstrass椭圆函数表示。交换微分算子定义了超几何方程的推广。
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 Lapla- cian in this commuting family of differential operators is expressed by the Weierstrass elliptic functions. The commuting differential operators define a generalization of hypergeometric equations.