Gelfand pairs and spherical functions.

Dieudonné, Jean

Displaying similar documents to “Gelfand pairs and spherical functions.”

Asymptotic spherical analysis on the Heisenberg group

Jacques Faraut (2010)

Colloquium Mathematicae

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The asymptotics of spherical functions for large dimensions are related to spherical functions for Olshanski spherical pairs. In this paper we consider inductive limits of Gelfand pairs associated to the Heisenberg group. The group K = U(n) × U(p) acts multiplicity free on 𝓟(V), the space of polynomials on V = M(n,p;ℂ), the space of n × p complex matrices. The group K acts also on the Heisenberg group H = V × ℝ. By a result of Carcano, the pair (G,K) with G = K ⋉ H is a Gelfand pair....

A Treatise on Spherical Trigonometry

John Hymers

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Spingroups and spherical means III

Sommen, F.

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Spectra for Gelfand pairs associated with the Heisenberg group

Chal Benson, Joe Jenkins, Gail Ratcliff, Tefera Worku (1996)

Colloquium Mathematicae

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Let K be a closed Lie subgroup of the unitary group U(n) acting by automorphisms on the (2n+1)-dimensional Heisenberg group $H_{n}$ . We say that $(K, H_{n})$ is a Gelfand pair when the set $L_{K}^{1} (H_{n})$ of integrable K-invariant functions on $H_{n}$ is an abelian convolution algebra. In this case, the Gelfand space (or spectrum) for $L_{K}^{1} (H_{n})$ can be identified with the set $Δ (K, H_{n})$ of bounded K-spherical functions on $H_{n}$ . In this paper, we study the natural topology on $Δ (K, H_{n})$ given by uniform convergence on compact subsets in $H_{n}$ . We show that...

Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

Sundaram Thangavelu (1991)

Revista Matemática Iberoamericana

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The aim of this paper is to study mean value operators on the reduced Heisenberg group H/Γ, where H is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of H.

Spherical unitary dual of general linear group over non-Archimidean local field

Marko Tadic (1986)

Annales de l'institut Fourier

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Let $F$ be a local non-archimedean field. The set of all equivalence classes of irreducible spherical representations of $G L (n, F)$ is described in the first part of the paper. In particular, it is shown that each irreducible spherical representation is parabolically induced by an unramified character. Bernstein’s result on the irreducibility of the parabolically induced representations of $G L (n, F)$ by irreducible unitary ones, and Ol’shanskij’s construction of complementary series give directly a description...

Spherical quadrangles.

Avelino, Catarina P., Breda, A.M.d&#039;Azevedo, Santos, Altino F. (2010)

Beiträge zur Algebra und Geometrie

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