Berezin-Weyl quantization for Cartan motion groups

Benjamin Cahen

Displaying similar documents to “Berezin-Weyl quantization for Cartan motion groups”

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...

The Weyl group as fixed point set of smooth involutions.

De Mari, Filippo (1996)

Journal of Lie Theory

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Geometry of biinvariant subsets of complex semisimple Lie groups

Gregor Fels, Laura Geatti (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Quantification of coadjoint orbits and the theory of contractions. (Quantification d'orbites coadjointes et théorie des contractions.)

Cahen, Benjamin (2001)

Journal of Lie Theory

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Invariant symbolic calculus for compact Lie groups

Benjamin Cahen (2019)

Archivum Mathematicum

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We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.

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...