G. I. Olshanskii, “Probability Measures on Dual Objects to Compact Symmetric Spaces and Hypergeometric Identities”, Funktsional. Anal. i Prilozhen., 37:4 (2003), 49–73; Funct. Anal. Appl., 37:4 (2003), 281

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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 4, Pages 49–73
DOI: https://doi.org/10.4213/faa168 (Mi faa168)

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

Probability Measures on Dual Objects to Compact Symmetric Spaces and Hypergeometric Identities

G. I. Olshanskii

Institute for Information Transmission Problems, Russian Academy of Sciences

Full-text PDF (302 kB) Citations (10)

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DOI: https://doi.org/10.4213/faa168

Abstract: We derive, in several different ways, combinatorial identities which are multidimensional analogs of classical Dougall's formula for a bilateral hypergeometric series of the type

_{2} H_{2}

${}_2H_2$ . These identities have a representation-theoretic meaning. They make it possible to construct concrete examples of spherical functions on inductive limits of symmetric spaces. These spherical functions are of interest to harmonic analysis.

Keywords: Dougall's formula, bilateral hypergeometric series, spherical functions, symmetric spaces.

Received: 10.09.2003

English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 4, Pages 281–301
DOI: https://doi.org/10.1023/B:FAIA.0000015579.81046.cb

Bibliographic databases:

Document Type: Article

UDC: 517.986.68+519.117

Language: Russian

Citation: G. I. Olshanskii, “Probability Measures on Dual Objects to Compact Symmetric Spaces and Hypergeometric Identities”, Funktsional. Anal. i Prilozhen., 37:4 (2003), 49–73; Funct. Anal. Appl., 37:4 (2003), 281–301

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa168

https://doi.org/10.4213/faa168

https://www.mathnet.ru/eng/faa/v37/i4/p49

This publication is cited in the following 10 articles:

Olshanski G., “Macdonald Polynomials and Extended Gelfand-Tsetlin Graph”, Sel. Math.-New Ser., 27:3 (2021), 41
Grigori Olshanski, “Macdonald-Level Extension of Beta Ensembles and Large-N Limit Transition”, Commun. Math. Phys., 385:1 (2021), 595
Guionnet A. Huang J., “Rigidity and Edge Universality of Discrete Beta-Ensembles”, Commun. Pure Appl. Math., 72:9 (2019), 1875–1982
Borodin A., Gorin V., Guionnet A., “Gaussian Asymptotics of Discrete Beta-Ensembles”, Publ. Math. IHES, 2017, no. 125, 1–78
Gorin V., Olshanski G., “a Quantization of the Harmonic Analysis on the Infinite-Dimensional Unitary Group”, J. Funct. Anal., 270:1 (2016), 375–418
Fyodorov Ya.V., Le Doussal P., “Moments of the Position of the Maximum for GUE Characteristic Polynomials and for Log-Correlated Gaussian Processes”, J. Stat. Phys., 164:1 (2016), 190–240
J. Math. Sci. (N. Y.), 215:6 (2016), 755–768
V. Gorin, G. I. Olshanskii, “Determinantal Measures Related to Big $q$ -Jacobi Polynomials”, Funct. Anal. Appl., 49:3 (2015), 214–217
G. I. Olshanskii, A. A. Osinenko, “Multivariate Jacobi Polynomials and the Selberg Integral”, Funct. Anal. Appl., 46:4 (2012), 262–278
S. V. Kerov, “Multidimensional hypergeometric distribution, and characters of the unitary group”, J. Math. Sci. (N. Y.), 129:2 (2005), 3697–3729

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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