Infinite-dimensional classical groups of finite \(r\)-rank: description of representations and asymptotic theory

DOI10.1007/BF01076358zbMath0545.22020MaRDI QIDQ797715

Grigori Olshanski

Publication date: 1984

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

zbMATH Keywords

unitary representationsrank

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items

Schur-Weyl Theory for C *-algebras, Infinite symmetric groups and combinatorial constructions of topological field theory type, Conical representations for direct limits of symmetric spaces, Diagonal locally finite Lie algebras and a version of Ado's theorem, On representations of the infinite symmetric group, A product on double cosets of \(B_\infty\), Grigori Iosifovich Olshanski, Groups of measure preserving transformations, Integrability of unitary representations on reproducing kernel spaces, Limit transition between hypergeometric functions of type BC and type A, Finitary simple Lie algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytic vectors
• Deformations of bouquets of quasihomogeneous one-dimensional singularities
• On a certain class of irreducible unitary representations of the infinite dimensional rotation group. I
• A series of unitary irreducible representations induced from a symmetric subgroup of a semisimple Lie group
• Kolmogorov's extension theorem for infinite measures
• Gaussian measure on the projective limit space of spheres