Displaying similar documents to “An extension of deLeeuw’s theorem to the n -dimensional rotation group”

An F. and M. Riesz theorem for bounded symmetric domains

R. G. M. Brummelhuis (1987)

Annales de l'institut Fourier

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We generalize the classical F. and M. Riesz theorem to metrizable compact groups whose center contains a copy of the circle group. Important examples of such groups are the isotropy groups of the bounded symmetric domains. The proof uses a criterion for absolute continuity involving L p spaces with p < 1 : A measure μ on a compact metrisable group K is absolutely continuous with respect to Haar measure d k on K if for some p < 1 a certain subspace of L p ( K , d k ) which is related to μ has sufficiently...

On a variant of Kazhdan's property (T) for subgroups of semisimple groups

Mohammed Bachir Bekka, Nicolas Louvet (1997)

Annales de l'institut Fourier

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Let Γ be an irreducible lattice in a product G of simple groups. Assume that G has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of Γ in terms of the topology of the dual space G ^ of G . We use this result to give a new proof for the triviality of the first cohomology group of Γ with coefficients in a finite dimensional unitary representation.

An inequality for local unitary Theta correspondence

Z. Gong, L. Grenié (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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Given a representation π of a local unitary group G and another local unitary group H , either the Theta correspondence provides a representation θ H ( π ) of H or we set θ H ( π ) = 0 . If G is fixed and H varies in a Witt tower, a natural question is: for which H is θ H ( π ) ≠ 0 ? For given dimension m there are exactly two isometry classes of unitary spaces that we denote H m ± . For ε ∈ { 0 , 1 } let us denote m ε ± ( π ) the minimal m of the same parity of ε such that θ H m ± ( π ) ≠ 0 , then we prove that m ε + ( π ) + m ε - ( π ) ≥ 2 n + 2 where n is the dimension of π .

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let G be a quasi-Hermitian Lie group with Lie algebra 𝔤 and K be a compactly embedded subgroup of G . Let ξ 0 be a regular element of 𝔤 * which is fixed by K . We give an explicit G -equivariant diffeomorphism from a complex domain onto the coadjoint orbit 𝒪 ( ξ 0 ) of ξ 0 . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where 𝒪 ( ξ 0 ) is associated with a unitary irreducible representation of G which...

On group representations whose C * algebra is an ideal in its von Neumann algebra

Edmond E. Granirer (1979)

Annales de l'institut Fourier

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Let τ be a continuous unitary representation of the locally compact group G on the Hilbert space H τ . Let C τ * [ V N τ ] be the C * [ W * ] algebra generated by ( L 1 ( G ) ) and M τ ( C τ * ) = φ ∈ V N τ ; φ C τ * + C τ * φ ⊂ C τ * . The main result obtained in this paper is Theorem 1: If G is σ -compact and M τ ( C τ * ) = V N τ then supp τ is discrete and each π in supp τ in CCR. We apply this theorem to the quasiregular representation τ = π H and obtain among other results that M π H ( C π H * ) = V N π H implies in many cases that G / H is a compact coset space.