Abstract:
The problem of restricting a highest weight representation of the group U(p,q) to the subgroup O(p,q) is considered. This restriction has an intricate spectrum that contains representations of different types. We construct a decomposition of this representation into reducible representations each of which
has a single-type spectrum.
Some integrals over classical groups are also calculated; these integrals generalize those of Hua.
Citation:
Yu. A. Neretin, “On the Separation of Spectra in the Analysis of Berezin Kernels”, Funktsional. Anal. i Prilozhen., 34:3 (2000), 49–62; Funct. Anal. Appl., 34:3 (2000), 197–207
\Bibitem{Ner00}
\by Yu.~A.~Neretin
\paper On the Separation of Spectra in the Analysis of Berezin Kernels
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 3
\pages 49--62
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\crossref{https://doi.org/10.4213/faa311}
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\zmath{https://zbmath.org/?q=an:0967.22007}
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\transl
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 3
\pages 197--207
\crossref{https://doi.org/10.1007/BF02482409}
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Linking options:
https://www.mathnet.ru/eng/faa311
https://doi.org/10.4213/faa311
https://www.mathnet.ru/eng/faa/v34/i3/p49
This publication is cited in the following 15 articles:
Ryosuke Nakahama, “Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval–Plancherel-Type Formulas under Subgroups”, SIGMA, 19 (2023), 049, 74 pp.
Neretin Yu.A., “Projections Separating Spectra For l-2 on Pseudounitary Groups U(P, Q)”, Int. Math. Res. Notices, 2019:17 (2019), 5256–5283
Krantz S., “Harmonic and Complex Analysis in Several Variables”, Harmonic and Complex Analysis in Several Variables, Springer Monographs in Mathematics, Springer, 2017, 1–424
Steven G. Krantz, Springer Monographs in Mathematics, Harmonic and Complex Analysis in Several Variables, 2017, 395
Merigon S., Seppaenen H., “Branching laws for discrete Wallach points”, Journal of Functional Analysis, 258:10 (2010), 3241–3265
J. Math. Sci. (N. Y.), 141:4 (2007), 1452–1478
Yu. A. Neretin, “Rayleigh triangles and non-matrix interpolation of matrix beta integrals”, Sb. Math., 194:4 (2003), 515–540
Yu. A. Neretin, “Beta functions of Bruhat–Tits buildings and deformation of l2
on the set of p-adic lattices”, Sb. Math., 194:12 (2003), 1775–1805
Olshanski, G, “The problem of harmonic analysis on the infinite-dimensional unitary group”, Journal of Functional Analysis, 205:2 (2003), 464
Ben Said, S, “Weighted Bergman spaces on bounded symmetric domains”, Pacific Journal of Mathematics, 206:1 (2002), 39
Neretin, YA, “Hua-type integrals over unitary groups and over projective limits of unitary groups”, Duke Mathematical Journal, 114:2 (2002), 239
Neretin, YA, “Plancherel formula for Berezin deformation of L-2 on Riemannian symmetric space”, Journal of Functional Analysis, 189:2 (2002), 336
Yu. A. Neretin, “Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces”, Sb. Math., 192:3 (2001), 403–432
Yu. A. Neretin, “Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants”, Mosc. Math. J., 1:2 (2001), 157–220
Borodin, A, “Infinite random matrices and ergodic measures”, Communications in Mathematical Physics, 223:1 (2001), 87
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