Geodesic
Invariant symbolic calculus for semidirect products
Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 2, pp. 253-269.

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Let $G$ be the semidirect product $V\rtimes \,K$ where $K$ is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space $V$. Let $\pi$ be a unitary irreducible representation of $G$ which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of $G$ whose little group is a maximal compact subgroup of $K$. We construct an invariant symbolic calculus for $\pi$, under some technical hypothesis. We give some examples including the Poincaré group.
DOI : 10.14712/1213-7243.2015.244
Classification : 22D30, 22E45, 22E46, 81R05, 81S10
Keywords: semidirect products; invariant symbolic calculus; coadjoint orbit; unitary representation; Berezin quantization; Weyl quantization; Poincaré group 
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Cahen, Benjamin. Invariant symbolic calculus for semidirect products. Commentationes Mathematicae Universitatis Carolinae, Tome 59 (2018) no. 2, pp. 253-269. doi : 10.14712/1213-7243.2015.244. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.244/

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