Journal of Lie Theory 19 (2009), No. 2, 291--310
Copyright Heldermann Verlag 2009
Contraction of Discrete Series via Berezin Quantization
Benjamin Cahen
Dép. de Mathématiques, LMMAS -- ISGMP-Bat. A, Ile du Saulcy, 57045 Metz 01, France
cahen@math.univ-metz.fr
We establish and study a contraction of the holomorphic discrete series representations of a non-compact semi-simple Lie group to the unitary irreducible representations of a Heisenberg group by means of Berezin quantization.
Keywords: Contraction of representations, holomorphic discrete series, semisimple Lie group, reproducing kernel Hilbert space, coherent states, Berezin quantization, Berezin symbols.
MSC: 22E46, 81R30, 46E22
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