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Title: Stratonovich-Weyl correspondence via Berezin quantization
Authors: Cahen, Benjamin
Keywords: Stratonovich-Weyl correspondenceBerezin quantizationBerezin transformquasi-Hermitian Lie groupcoadjoint orbitunitary representationholomorphic representationreproducing kernel Hilbert spaceHeisenberg motion group
Issue Date: 23-Dec-2014
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
46 (2014)
Let G be a quasi-Hermitian Lie group and let K be a maximal compactly embedded subgroup of G. Let π be aunitary representation of G which is holomorphically induced from a unitary representation ρ of K. We introduce and study a notion of complex-valued Berezin symbol for an operator acting on the space of π and the corresponding notion of Stratonovich-Weyl correspondence. This generalizes some results already obtained in the case when ρ is an unitary character, see [19]. As an example, we treat in detail the case of the Heisenberg motion groups.
Benjamin Cahen, "Stratonovich-Weyl correspondence via Berezin quantization", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 46 (2014), pp.157-180
Type: Article
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.46 (2014)

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