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
dijk@math.leidenuniv.nl
Michael Pevzner
Lab. de Mathématiques, Université de Reims, Campus Moulin de la Housse, BP 1039, 51687 Reims, France
pevzner@univ-reims.fr
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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