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Algebra i Analiz, 2000, Volume 12, Issue 5, Pages 28–63 (Mi aa1121)  

This article is cited in 20 scientific papers (total in 20 papers)

Research Papers

Harmonic analysis on the infinite symmetric group, and the Whittaker kernel

A. M. Borodinab

a Institute for Information Transmission Problems, Russian Academy of Sciences
b Department of Mathematics, The University of Pennsylvania, Philadelphia, USA

Full text: PDF file (1535 kB)

English version:
St. Petersburg Mathematical Journal, 2001, 12:5, 733–759

Bibliographic databases:

Received: 09.03.1999

Citation: A. M. Borodin, “Harmonic analysis on the infinite symmetric group, and the Whittaker kernel”, Algebra i Analiz, 12:5 (2000), 28–63; St. Petersburg Math. J., 12:5 (2001), 733–759

Citation in format AMSBIB
\Bibitem{Bor00}
\by A.~M.~Borodin
\paper Harmonic analysis on the infinite symmetric group, and the Whittaker kernel
\jour Algebra i Analiz
\yr 2000
\vol 12
\issue 5
\pages 28--63
\mathnet{http://mi.mathnet.ru/aa1121}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1812941}
\zmath{https://zbmath.org/?q=an:0988.43010}
\transl
\jour St. Petersburg Math. J.
\yr 2001
\vol 12
\issue 5
\pages 733--759


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

    This publication is cited in the following articles:
    1. Borodin A., Deift P., “Fredholm determinants, Jimbo-Miwa-Ueno $\tau$-functions, and representation theory”, Comm. Pure Appl. Math., 55:9 (2002), 1160–1230  crossref  mathscinet  zmath  isi  scopus
    2. Borodin A., “Asymptotic representation theory and Riemann–Hilbert problem”, Asymptotic combinatorics with applications to mathematical physics (St. Petersburg, 2001), Lecture Notes in Math., 1815, Springer, Berlin, 2003, 3–19  crossref  mathscinet  zmath  isi
    3. Olshanski C., “An introduction to harmonic analysis on the infinite symmetric group”, Asymptotic combinatorics with applications to mathematical physics (St. Petersburg, 2001), Lecture Notes in Math., 1815, Springer, Berlin, 2003, 127–160  crossref  mathscinet  zmath  isi
    4. Borodin A., “Discrete gap probabilities and discrete Painlevé equations”, Duke Math. J., 117:3 (2003), 489–542  crossref  mathscinet  zmath  isi  scopus
    5. Olshanski G., “The problem of harmonic analysis on the infinite–dimensional unitary group”, Journal of Functional Analysis, 205:2 (2003), 464–524  crossref  mathscinet  zmath  isi  scopus
    6. Olshanski G., “Point processes related to the infinite symmetric group”, Orbit Method in Geometry and Physics – in Honor of A.A. Kirillov, Progress in Mathematics, 213, 2003, 349–393  mathscinet  zmath  isi
    7. Kerov S., Olshanski G., Vershik A., “Harmonic analysis on the infinite symmetric group”, Invent. Math., 158:3 (2004), 551–642  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Borodin A., Olshanski G., “Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes”, Ann. of Math. (2), 161:3 (2005), 1319–1422  crossref  mathscinet  zmath  isi  scopus
    9. Borodin A., Olshanski G., “$Z$-measures on partitions and their scaling limits”, European J. Combin., 26:6 (2005), 795–834  crossref  mathscinet  zmath  isi  elib  scopus
    10. Borodin A., Olshanski G., “Random partitions and the gamma kernel”, Adv. Math., 194:1 (2005), 141–202  crossref  mathscinet  zmath  isi  elib  scopus
    11. Borodin A., Olshanski G., “Representation theory and random point processes”, European Congress of Mathematics, 2005, 73–94  mathscinet  zmath  isi
    12. Borodin A., Olshanski G., Strahov E., “Giambelli compatible point processes”, Adv. in Appl. Math., 37:2 (2006), 209–248  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Borodin A., Olshanski G., “Markov processes on partitions”, Probab. Theory Related Fields, 135:1 (2006), 84–152  crossref  mathscinet  zmath  isi  elib  scopus
    14. Borodin A., Olshanski G., “Infinite-dimensional diffusions as limits of random walks on partitions”, Probab. Theory Related Fields, 144:1-2 (2009), 281–318  crossref  mathscinet  zmath  isi  elib  scopus
    15. Borodin A., Strahov E., “Correlation kernels for discrete symplectic and orthogonal ensembles”, Comm. Math. Phys., 286:3 (2009), 933–977  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. Strahov E., “$Z$-measures on partitions related to the infinite Gelfand pair $(S(2\infty),H(\infty))$”, J. Algebra, 323:2 (2010), 349–370  crossref  mathscinet  zmath  isi  elib  scopus
    17. Olshanski G., “Anisotropic Young Diagrams and Infinite–Dimensional Diffusion Processes with the Jack Parameter”, International Mathematics Research Notices, 2010, no. 6, 1102–1166  mathscinet  zmath  isi  elib
    18. Strahov E., “The z–measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel”, Advances in Mathematics, 224:1 (2010), 130–168  crossref  mathscinet  zmath  isi  scopus
    19. Petrov L., “Sl(2) Operators and Markov Processes on Branching Graphs”, J. Algebr. Comb., 38:3 (2013), 663–720  crossref  mathscinet  zmath  isi  elib  scopus
    20. Borodin A., Olshanski G., “Markov Dynamics on the Thoma Cone: a Model of Time-Dependent Determinantal Processes with Infinitely Many Particles”, Electron. J. Probab., 18 (2013), 75, 1–43  crossref  mathscinet  isi  scopus
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