The Poisson model of the Fock space and representations of current groups

DOI10.1090/S1061-0022-2012-01204-5zbMath1256.81058MaRDI QIDQ2892179

Anatoly M. Vershik, Mark I. Graev

Publication date: 18 June 2012

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Fock representationcanonical representationinfinite-dimensional Lebesgue measurespecial representationcurrent groupintegral model

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Many-body theory; quantum Hall effect (81V70) Applications of group representations to physics and other areas of science (20C35)

Related Items (4)

Nonsingular Poisson suspensions ⋮ Nonunitary representations of the groups of \(U(p, q)\)-currents for \(q\geq p > 1\) ⋮ Special representations of the Iwasawa subgroups of simple Lie groups ⋮ Cohomology in nonunitary representations of semisimple Lie groups (the group \(U(2,2)\))

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
• A commutative model of a representation of the group \(O(n, 1)^{X}\) and a generalized Lebesgue measure in the space of distributions
• Canonical representations and overgroups for hyperboloids
• The behavior of the Laplace transform of the invariant measure on the hypersphere of high dimension
• Invariant measures for the continual Cartan subgroup
• Integral models of representations of current groups
• Integral models of unitary representations of current groups with values in semidirect products
• Irréductibilité de certaines représentations de \(G^{(x)}\)
• Does there exist a Lebesgue measure in the infinite-dimensional space?
• Positive definite kernels, continuous tensor products, and central limit theorems of probability theory
• 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
• Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
• Structure of the complementary series and special representations of the groupsO(n,1) andU(n,1)
• Integral models of representations of the current groups of simple Lie groups
• Unitary representations of maximal parabolic subgroups of the classical groups
• 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations
• Examples of Nonlinear Continuous Tensor Products of Measure Spaces and Non-Fock Factorizations
• 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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