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Journal of Lie Theory 17 (2007), No. 2, 283--305
Copyright Heldermann Verlag 2007

Ring Structures for Holomorphic Discrete Series and Rankin-Cohen Brackets

Gerrit van Dijk
Mathematisch Instituut,, Universiteit Leiden, PO Box 9512, 2300 RA Leiden, Netherlands

Michael Pevzner
Lab. de Mathématiques, Université de Reims, Campus Moulin de la Housse, BP 1039, 51687 Reims, France

We discuss two different ring structures on the set of holomorphic discrete series of a causal symmetric space of Cayley type G/H and we suggest a new interpretation of Rankin-Cohen brackets in terms of intertwining operators arising in the decomposition of tensor products of holomorphic discrete series representations.

Keywords: Discrete series representations, covariant quantization, para-Hermitian symmetric spaces, Rankin-Cohen brackets.

MSC: 22E46, 43A85, 11F60

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