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...

On representations of restricted Lie superalgebras

Yu-Feng Yao (2014)

Czechoslovak Mathematical Journal

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Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type $A (n | 0)$ , the baby Verma modules $Z_{χ} (λ)$ are proved to be simple for any regular nilpotent $p$ -character $χ$ and typical weight $λ$ . Moreover, we obtain the dimension formulas for projective covers of simple modules with $p$ -characters of standard Levi form.

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

On representations of restricted Lie superalgebras

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