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Mat. Sb., 2003, Volume 194, Number 4, Pages 49–74 (Mi msb727)  

This article is cited in 10 scientific papers (total in 10 papers)

Rayleigh triangles and non-matrix interpolation of matrix beta integrals

Yu. A. Neretin

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: A Rayleigh triangle of size $n$ is a set of $n(n+1)/2$ real numbers $\lambda_{kl}$, where $1\leqslant l\leqslant k\leqslant n$, which are decreasing as $k$ increases for fixed $k$ and are increasing as $k$ increases for fixed $k-l$. We construct a family of beta integrals over the space of Rayleigh triangles which interpolate matrix integrals of the types of Siegel, Hua Loo Keng, and Gindikin with respect to the dimension of the ground field ($\mathbb R$$\mathbb C$, or the quaternions $\mathbb H$). We also interpolate the Hua–Pickrell measures on the inverse limits of the symmetric spaces $\operatorname U(n)$, $\operatorname U(n)/\operatorname O(n)$, $\operatorname U(2n)/\operatorname{Sp}(n)$.
Our family of integrals also includes the Selberg integral.

DOI: https://doi.org/10.4213/sm727

Full text: PDF file (389 kB)
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English version:
Sbornik: Mathematics, 2003, 194:4, 515–540

Bibliographic databases:

UDC: 519.46
MSC: Primary 22E30, 43A85; Secondary 33C67, 43A80, 44A15
Received: 08.07.2002

Citation: Yu. A. Neretin, “Rayleigh triangles and non-matrix interpolation of matrix beta integrals”, Mat. Sb., 194:4 (2003), 49–74; Sb. Math., 194:4 (2003), 515–540

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. I. Olshanskii, “Probability Measures on Dual Objects to Compact Symmetric Spaces and Hypergeometric Identities”, Funct. Anal. Appl., 37:4 (2003), 281–301  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Peter J. Forrester, Eric M. Rains, “Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices”, Internat Math Res Notices, 2006, 48306  crossref  mathscinet  zmath  isi
    3. Olshanski G., “Projections of Orbital Measures, Gelfand-Tsetlin Polytopes, and Splines”, J. Lie Theory, 23:4 (2013), 1011–1022  mathscinet  zmath  isi  elib
    4. Vadim Gorin, “From Alternating Sign Matrices to the Gaussian Unitary Ensemble”, Commun. Math. Phys, 2014  crossref  mathscinet
    5. Alexei Borodin, Vadim Gorin, “Generalβ-Jacobi corners process and the Gaussian free field”, Commun. Pur. Appl. Math, 2014, n/a  crossref  mathscinet
    6. Vadim Gorin, Mykhaylo Shkolnikov, “Multilevel Dyson Brownian motions via Jack polynomials”, Probab. Theory Relat. Fields, 2014  crossref  mathscinet
    7. Y. A. Neretin, “Hua-Type Beta-Integrals and Projective Systems of Measures on Flag Spaces”, International Mathematics Research Notices, 2015  crossref  mathscinet
    8. Sun Y., “a New Integral Formula For Heckman-Opdam Hypergeometric Functions”, Adv. Math., 289 (2016), 1157–1204  crossref  mathscinet  zmath  isi
    9. Gorin V., Shkolnikov M., “Interacting Particle Systems At the Edge of Multilevel Dyson Brownian Motions”, Adv. Math., 304 (2017), 90–130  crossref  mathscinet  zmath  isi  elib  scopus
    10. Cuenca C., “Pieri Integral Formula and Asymptotics of Jack Unitary Characters”, Sel. Math.-New Ser., 24:3 (2018), 2737–2789  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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