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Rankin–Cohen brackets and representations of conformal Lie groups

Michael Pevzner (2012)

Annales mathématiques Blaise Pascal

This is an extended version of a lecture given by the author at the summer school “Quasimodular forms and applications” held in Besse in June 2010.The main purpose of this work is to present Rankin-Cohen brackets through the theory of unitary representations of conformal Lie groups and explain recent results on their analogues for Lie groups of higher rank. Various identities verified by such covariant bi-differential operators will be explained by the associativity of a non-commutative product...

Rapidly decreasing functions on general semisimple groups

Rebecca A. Herb, Joseph A. Wolf (1986)

Compositio Mathematica

Rechtsdistributive Multiplikationen auf homogenen Räumen.

Karl Strambach (1987)

Journal für die reine und angewandte Mathematik

Reducibility of Unramified Unitary Principal Series Representations of p-Adic Groups and Class-1 Representations.

D. Keys (1982)

Mathematische Annalen

Relative discrete series of line bundles over bounded symmetric domains

Anthony H. Dooley, Bent Ørsted, Genkai Zhang (1996)

Annales de l'institut Fourier

We study the relative discrete series of the $L^{2}$ -space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.