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...

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...