Invariant differential operators on the tangent space of some symmetric spaces

Thierry Levasseur; J. Toby Stafford

Displaying similar documents to “Invariant differential operators on the tangent space of some symmetric spaces”

The kernel of an homomorphism of Harish-Chandra

T. Levasseur, J. T. Stafford (1996)

Annales scientifiques de l'École Normale Supérieure

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The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties

Dmitrii I. Panyushev (1994)

Compositio Mathematica

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Cohomology of $G / P$ for classical complex Lie supergroups $G$ and characters of some atypical $G$ -modules

Ivan Penkov, Vera Serganova (1989)

Annales de l'institut Fourier

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We compute the unique nonzero cohomology group of a generic $G^{0}$ - linearized locally free $𝒪$ -module, where $G^{0}$ is the identity component of a complex classical Lie supergroup $G$ and $P ↪ G^{0}$ is an arbitrary parabolic subsupergroup. In particular we prove that for $G \neq ℙ (m), S ℙ (m)$ this cohomology group is an irreducible $G^{0}$ -module. As an application we generalize the character formula of typical irreducible $G^{0}$ -modules to a natural class of atypical modules arising in this way.

$D$ -modules and representation theory of Lie groups

Masaki Kashiwara (1993)

Annales de l'institut Fourier

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On the $K$ -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

Patrick Polo (1995)

Annales de l'institut Fourier

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Let $G$ be a semisimple complex algebraic group and $X$ its flag variety. Let $𝔤 = Lie (G)$ and let $U$ be its enveloping algebra. Let $𝔥$ be a Cartan subalgebra of $𝔤$ . For $μ \in 𝔥^{*}$ , let $J_{μ}$ be the corresponding minimal primitive ideal, let $U_{μ} = U / J_{μ}$ , and let $𝒯_{U_{μ}} : K_{0} (U_{m} u) \to ℂ$ be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the $ℂ$ -algebras $U_{μ}$ . When $μ$ is regular, Hodges has shown that $K_{0} (U_{μ}) ≅ K_{0} (X)$ . In this case $K_{0} (U_{μ})$ is generated by the classes corresponding...

Displaying similar documents to “Invariant differential operators on the tangent space of some symmetric spaces”

The kernel of an homomorphism of Harish-Chandra

The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties

Cohomology of G / P for classical complex Lie supergroups G and characters of some atypical G -modules

D -modules and representation theory of Lie groups

On the K -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

Cohomology of $G / P$ for classical complex Lie supergroups $G$ and characters of some atypical $G$ -modules

$D$ -modules and representation theory of Lie groups

On the $K$ -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case