The basic representation of the current group \(O(n,1)^X\) in the \(L^2\) space over the generalized Lebesgue measure

DOI10.1016/S0019-3577(05)80038-2zbMath1147.22013arXivmath/0503404OpenAlexW2093682117MaRDI QIDQ855598

Mark I. Graev, Anatoly M. Vershik

Publication date: 7 December 2006

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503404

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

Related Items (7)

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 representations of current groups ⋮ Integral models of unitary representations of current groups with values in semidirect products

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A commutative model of presentation of the group of flows \(SL(2,R)^ X\) that is connected with a unipotent subgroup
• Irreducible representations of the group \(G^X\) and cohomologies
• 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
• 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
• COHOMOLOGY OF GROUPS IN UNITARY REPRESENTATIONS, THE NEIGHBORHOOD OF THE IDENTITY, AND CONDITIONALLY POSITIVE DEFINITE FUNCTIONS
• Spherical functions and characters on the groupU(∞)^X
• 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

This page was built for publication: The basic representation of the current group \(O(n,1)^X\) in the \(L^2\) space over the generalized Lebesgue measure