Rings of regular functions on nilpotent orbits 11:model algebras and orbits

DOI10.1080/00927879408824874zbMath0813.22006OpenAlexW2009698105MaRDI QIDQ4288236

William M. McGovern

Publication date: 6 June 1994

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879408824874

zbMATH Keywords

multiplicityLie algebraenveloping algebrahighest weightnilpotent orbitweight multiplicitiesfinite-dimensional representationcomplex simply connected semisimple Lie groupDixmier algebraBernstein-Gelfand-Gelfand theory of model representationscoordinate ring of regular functions

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46) General properties and structure of complex Lie groups (22E10)

Related Items (14)

Unnamed Item ⋮ On the coordinate ring of spherical conjugacy classes. ⋮ Dirac series for complex \(E_7\) ⋮ Representations associated to small nilpotent orbits for complex Spin groups ⋮ Unnamed Item ⋮ Enveloping algebras of Slodowy slices and Goldie rank ⋮ Spherical conjugacy classes and involutions in the Weyl group ⋮ Unitary representations with non-zero Dirac cohomology for complex \(E_{6}\) ⋮ Representations associated to small nilpotent orbits for real Spin groups ⋮ Unnamed Item ⋮ On quantization of a nilpotent orbit closure in $G_2$ ⋮ Unitary representations with Dirac cohomology: a finiteness result for complex Lie groups ⋮ On a Conjecture of Barbasch and Pandžić ⋮ Spherical nilpotent orbits and the Kostant-Sekiguchi correspondence

Cites Work

• Unnamed Item
• Unnamed Item
• A branching law for \(Spin(7,{\mathbb{C}})\to G_ 2\) and its applications to unipotent representations
• Rings of regular functions on nilpotent orbits and their covers
• Models of representations of compact Lie groups
• Modèle de Whittaker et ideaux primitifs complètement premiers dans les algèbres enveloppantes des algèbres de Lie semisimples complexes II.
• Classes of unipotent elements in simple algebraic groups. II

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