Isotropy representation of flag manifolds

Alekseevsky, D. V.

Displaying similar documents to “Isotropy representation of flag manifolds”

Flag Manifolds

D. V. Alekseevsky (1997)

Zbornik Radova

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Algorithmic computations of Lie algebras cohomologies

Šilhan, Josef

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From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package $L i E$ offers the data structures and corresponding procedures for...

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.

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let $G$ be a quasi-Hermitian Lie group with Lie algebra $𝔤$ and $K$ be a compactly embedded subgroup of $G$ . Let $ξ_{0}$ be a regular element of $𝔤^{*}$ which is fixed by $K$ . We give an explicit $G$ -equivariant diffeomorphism from a complex domain onto the coadjoint orbit $𝒪 (ξ_{0})$ of $ξ_{0}$ . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where $𝒪 (ξ_{0})$ is associated with a unitary irreducible representation of $G$ which...

Displaying similar documents to “Isotropy representation of flag manifolds”

Flag Manifolds

Algorithmic computations of Lie algebras cohomologies

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

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

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