Sphericity and multiplication of double cosets for infinite-dimensional classical groups

DOI10.1007/s10688-011-0025-6zbMath1271.22019arXiv1101.4759OpenAlexW2060138458MaRDI QIDQ366317

Yuriĭ A. Neretin

Publication date: 12 September 2013

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.4759

zbMATH Keywords

unitary representationinner functionspherical functionspherical subgroupcategory representationcharacteristic function (transfer function)operator colligation

Mathematics Subject Classification ID

Analysis on and representations of infinite-dimensional Lie groups (22E66)

Related Items (11)

Several remarks on groups of automorphisms of free groups ⋮ Infinite symmetric groups and combinatorial constructions of topological field theory type ⋮ Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument ⋮ Symmetries of Gaussian measures and operator colligations ⋮ The space \(L^2\) on semi-infinite Grassmannian over finite field ⋮ A product on double cosets of \(B_\infty\) ⋮ Multi-operator colligations and multivariate characteristic functions ⋮ Groups \(\mathrm{GL}(\infty)\) over finite fields and multiplications of double cosets ⋮ On the group of infinite \(p\)-adic matrices with integer elements ⋮ On spherical unitary representations of groups of spheromorphisms of Bruhat-Tits trees ⋮ Description of unitary representations of the group of infinite 𝑝-adic integer matrices

Cites Work

• Multi-operator colligations and multivariate characteristic functions
• Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
• The problem of harmonic analysis on the infinite-dimensional unitary group.
• Separable representations for automorphism groups of infinite symmetric spaces
• Hua-type integrals over unitary groups and over projective limits of unitary groups
• Infinite Tri-symmetric Group, Multiplication of Double Cosets, and Checker Topological Field Theories
• Spherical functions over a normed field whose residue field is infinite
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