Invariant Differential Operators and an Homomorphism of Harish-Chandra

DOI10.2307/2152821zbMath0837.22011OpenAlexW4239355982MaRDI QIDQ4846141

Thierry Levasseur, J. Toby Stafford

Publication date: 13 May 1996

Full work available at URL: https://doi.org/10.2307/2152821

zbMATH Keywords

Weyl groupdifferential operatorspolynomial functionsCartan subalgebraSpringer correspondencecomplex reductive Lie algebras

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Rings of differential operators (associative algebraic aspects) (16S32) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

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Cites Work

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• Fixed rings of finite automorphism groups of associative rings
• Invariant eigendistributions on a semisimple Lie algebra
• Rings of differential operators on classical rings of invariants
• Invariant Differential Operators on a Reductive Lie Algebra and Weyl Group Representations
• Differential Operators on a Semisimple Lie Algebra
• Invariant Differential Operators and Distributions on a Semisimple Lie Algebra