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

DOI10.1007/S10688-012-0001-9zbMath1279.22032OpenAlexW2049294710MaRDI QIDQ366040

Anatoly M. Vershik, Mark I. Graev

Publication date: 11 September 2013

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

Full work available at URL: https://doi.org/10.1007/s10688-012-0001-9

zbMATH Keywords

Fock representationcanonical representationspecial representationcurrent groupintegral model

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Analysis on and representations of infinite-dimensional Lie groups (22E66)

Related Items (2)

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 \(U(2,2)\))

Cites Work

• A commutative model of a representation of the group \(O(n, 1)^{X}\) and a generalized Lebesgue measure in the space of distributions
• Structure of the complementary series and special representations of the groupsO(n,1) andU(n,1)
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