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

Oshima Toshio; Sekiguchi Hideko

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

机译：在Weyl群的作用下通向不变微分算子族

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ForaWeylgroup$W$ofaclassicalrootsystem$(?￡,E)$,westudy$W$-invariantcommutingdifferentialoperatorson$E$whosehighestordertermsgeneratethe$W$-invariantdifferentialoperatorswithconstantcoefficients.WeshowthatthepotentialfunctionfortheLaplacianinthiscommutingfamilyofdifferentialoperatorsisexpressedbytheWeierstrassellipticfunctions.Thecommutingdifferentialoperatorsdefineageneralizationofhypergeometricequations.

机译：韦尔集团经典的根系统$（$ ￡，E）$，西元$ W $-不变的通勤差分算子$ E $（其最高阶条件生成具有不变系数的W $-不变的差动算子）。

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《Journal of mathematical sciences, The University of Tokyo》 |1995年第1期|共页
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Oshima Toshio; Sekiguchi Hideko;
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中图分类数学;
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Commuting families of differential operators invariant under the action of a Weyl group

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