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Journal of Lie Theory 28 (2018), No. 4, 1043--1062
Copyright Heldermann Verlag 2018

Stratonovich-Weyl Correspondence for the Generalized Poincaré Group

Benjamin Cahen
Université de Lorraine, Dép. de Mathématiques, 3 rue Augustin Fresnel, 57073 Metz Cedex 03, France


We construct a Stratonovich-Weyl correspondence for each unitary irreducible representation of the generalized Poincar\'e group $ {\mathbb R}^{n+1}\rtimes SO_0(n,1)$ associated with an integral coadjoint orbit with little group $SO(n)$, generalizing some results of J.\,F.\,Cari\~{n}ena, J.\,M.\,Gracia-Bond\`{i}a and J.\,C.\,V\`{a}rilly [J. Phys. A: Math. Gen. 23 (1990) 901--933].

Keywords: Poincaré group, coadjoint orbit, unitary representation, Weyl quantization, Berezin quantization, Stratonovich-Weyl correspondence.

MSC: 81S10, 22E46, 22E45, 81R05

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