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

Benjamin Cahen

Displaying similar documents to “Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group”

Weyl quantization for the semidirect product of a compact Lie group and a vector space

Benjamin Cahen (2009)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be the semidirect product $V ⋊ K$ where $K$ is a semisimple compact connected Lie group acting linearly on a finite-dimensional real vector space $V$ . Let $𝒪$ be a coadjoint orbit of $G$ associated by the Kirillov-Kostant method of orbits with a unitary irreducible representation $π$ of $G$ . We consider the case when the corresponding little group $H$ is the centralizer of a torus of $K$ . By dequantizing a suitable realization of $π$ on a Hilbert space of functions on $ℂ^{n}$ where $n = dim (K / H)$ , we construct a symplectomorphism...

Berezin transform for non-scalar holomorphic discrete series

Benjamin Cahen (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let $M = G / K$ be a Hermitian symmetric space of the non-compact type and let $π$ be a discrete series representation of $G$ which is holomorphically induced from a unitary irreducible representation $ρ$ of $K$ . In the paper [B. Cahen, Berezin quantization for holomorphic discrete series representations: the non-scalar case, Beiträge Algebra Geom., DOI 10.1007/s13366-011-0066-2], we have introduced a notion of complex-valued Berezin symbol for an operator acting on the space of $π$ . Here we study the corresponding...

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...