Integral models of representations of current groups

DOI10.1007/s10688-008-0002-xzbMath1162.22019OpenAlexW2088623945MaRDI QIDQ1002787

Anatoly M. Vershik, Mark I. Graev

Publication date: 26 February 2009

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

Full work available at URL: https://doi.org/10.1007/s10688-008-0002-x

zbMATH Keywords

current groupintegral of tensor productssummable representation

Mathematics Subject Classification ID

Loop groups and related constructions, group-theoretic treatment (22E67) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65)

Related Items (6)

The Poisson model of the Fock space and representations of current groups ⋮ Does there exist a Lebesgue measure in the infinite-dimensional space? ⋮ Nonunitary representations of the groups of \(U(p, q)\)-currents for \(q\geq p > 1\) ⋮ Cohomology in nonunitary representations of semisimple Lie groups (the group \(U(2,2)\)) ⋮ Invariant measures for the continual Cartan subgroup ⋮ Integral models of unitary representations of current groups with values in semidirect products

Cites Work

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• The basic representation of the current group \(O(n,1)^X\) in the \(L^2\) space over the generalized Lebesgue measure
• Any separable ultrametric space can be isometrically imbedded in \(l_ 2\)
• Does there exist a Lebesgue measure in the infinite-dimensional space?
• Factorizable representation of current algebra. Non commutative extension of the Levy-Kinchin formula and cohomology of a solvable group with values in a Hilbert space
• Structure of the complementary series and special representations of the groupsO(n,1) andU(n,1)
• Fock factorizations, and decompositions of theL²spaces over general Lévy processes
• An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process

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