Displaying similar documents to “Coherent states and square integrable representations”

Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu (1980)

Annales de l'institut Fourier

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We introduce a new class of connected solvable Lie groups called H -group. Namely a H -group is a connected solvable Lie group with center Z such that for some ℓ in the Lie algebra h of H , the symplectic for B ℓ on h / z given by ℓ ( [ x , y ] ) is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group G with center Z , such that the center of G / Rad G is finite, has discrete series if and only if G may be written as G = H S ' , H ∩ S = Z 0 , where H is a H -group with...

Geometric constructions and representations

Wolf, Joseph A.

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[For the entire collection see Zbl 0742.00067.]Let G be a connected semisimple Lie group with finite center. In this review article the author describes first the geometric realization of the discrete series representations of G on Dolbeault cohomology spaces and the tempered series of representations of G on partial Dolbeault cohomology spaces. Then he discusses his joint work with Wilfried Schmid on the construction of maximal globalizations of standard Zuckerman modules via geometric...