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

Benjamin Cahen

Displaying similar documents to “Weyl quantization for the semidirect product of a compact Lie group and a vector space”

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...

Berezin-Weyl quantization for Cartan motion groups

Benjamin Cahen (2011)

Commentationes Mathematicae Universitatis Carolinae

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We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].

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...

Stratonovich-Weyl correspondence for discrete series representations

Benjamin Cahen (2011)

Archivum Mathematicum

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Let $M = G / K$ be a Hermitian symmetric space of the noncompact type and let $π$ be a discrete series representation of $G$ holomorphically induced from a unitary character of $K$ . Following an idea of Figueroa, Gracia-Bondìa and Vàrilly, we construct a Stratonovich-Weyl correspondence for the triple $(G, π, M)$ by a suitable modification of the Berezin calculus on $M$ . We extend the corresponding Berezin transform to a class of functions on $M$ which contains the Berezin symbol of $d π (X)$ for $X$ in the Lie algebra $𝔤$ of...

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...