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Invariant symbolic calculus for semidirect products

Benjamin Cahen (2018)

Commentationes Mathematicae Universitatis Carolinae

Let G be the semidirect product V K where K is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space V . Let π 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 π , under some technical hypothesis. We give some examples including the Poincaré group.

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