A commutative model of a representation of the group \(O(n, 1)^{X}\) and a generalized Lebesgue measure in the space of distributions

DOI10.1007/s10688-005-0021-9zbMath1135.22018OpenAlexW1975433550MaRDI QIDQ883607

Anatoly M. Vershik, Mark I. Graev

Publication date: 5 June 2007

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

Full work available at URL: https://doi.org/10.1007/s10688-005-0021-9

zbMATH Keywords

unitary representationsbasic representationCurrent groupsmaximal unipotent subgroup

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Unitary representations of locally compact groups (22D10)

Related Items (4)

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 \(q\geq p > 1\) ⋮ Special representations of the groups \(U(\infty,1)\) and \(O(\infty,1)\) and the associated representations of the current groups \(U(\infty,1)^X\) and \(O(\infty,1)^X\) in quasi-Poisson spaces

Cites Work

• Any separable ultrametric space can be isometrically imbedded in \(l_ 2\)
• Canonical semigroups of states and cocycles for the group of automorphisms of a homogeneous tree
• Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group
• An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process
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