Ring structures for holomorphic discrete series and Rankin-Cohen brackets.

Gerrit van Dijk , Michael Pevzner (1)

1 LMR - Laboratoire de Mathématiques de Reims

n the present note 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.

Mots clés: Rankin-Cohen brackets; Discrete series representations; Covariant Quantization; Para-Hermitian symmetric spaces; Rankin-Cohen brackets.

Domaines: Théorie des représentations [math.RT]

Gerrit van Dijk, Michael Pevzner. Ring structures for holomorphic discrete series and Rankin-Cohen brackets.. Journal of Lie Theory, 2007, 17, pp.283-305. ⟨hal-00163350⟩