Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty),H(\infty))$

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1985

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G. Olshanski, Unitary representations of ( G , K ) (G,K) -pairs that are connected with the infinite symmetric group S ⁡ ( ∞ ) S(\infty) . (Russian) Algebra i Analiz 1 (1989), no. 4, 178–209; translation in Leningrad Math. J. 1 (1990), no. 4, 983–1014

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S. Kerov, G. Olshanski, A. Vershik, Harmonic analysis on the infinite symmetric group. A deformation of the regular representation, Comptes Rend. Acad. Sci. Paris, Sér. I vol 316 (1993) 773–778

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I. G. Macdonald, Symmetric functions and Hall polynomials. Second Edition, Oxford University Press, 1995

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A. Borodin, G. Olshanski, Point processes and the infinite symmetric group. Math. Res. Lett 5 (1998) 799–816

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A. Borodin, G. Olshanski, Distributions on partitions, point processes, and the hypergeometric kernel, Comm. Math. Phys. 211 (2000) 335–358

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A. Borodin, G. Olshanski, Harmonic functions on multiplicative graphs and interpolation polynomials, Electron. J. Combin. 7 (2000), Research Paper 28, 39 pp

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S. Kerov, Anisotropic Young diagrams and Jack symmetric functions, Funktsion. Anal. i. Prilozhen. 34 (1) (2000) 51–64 (in Russian)

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

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A. Borodin, G. Olshanski, z z -measures on partitions, Robinson-Schensted-Knuth correspondence, and β = 2 \beta=2 random matrix ensembles. Random matrix models and their applications, 71–94, Math. Sci. Res. Inst. Publ., 40, Cambridge Univ. Press, Cambridge, 2001

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A. Okounkov, SL ⁡ ( 2 ) {\rm SL}(2) and z z -measures, Random matrix models and their applications, 407–420, Math. Sci. Res. Inst. Publ., 40, Cambridge Univ. Press, Cambridge, 2001

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A. Okounkov, Infinite wedge and random partitions. Selecta Math. (N.S.) 7 (2001) 57–81

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A. Borodin, P. Deift, Fredholm determinants, Jimbo-Miwa-Ueno τ \tau -functions, and representation theory, Comm. Pure Appl. Math. 55 (2002) 1160–1230

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J. Pitman, Combinatorial stochastic processes. Lecture Notes for St. Flour Summer School, July 2002, available via http://stat.-www.berkeley.edu/users/pitman/

A. Borodin, G. Olshanski, Z Z -measures on partitions and their scaling limits, European J. Combin. 26 (2005) 795–834

2005

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A. Borodin, G. Olshanski, Meixner polynomials and random partitions, Moscow Math. Journal 6 (2006) 626-655

2006

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A. Borodin, G. Olshanski, E. Strahov, Giambelli compatible point processes, Adv. in Appl. Math. 37 (2006) 209–248

2006

Later among the works it cites.

A. M. Vershik, N. V. Tsilevich, On the Fourier transform on the infinite symmetric group. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 325 (2005), Teor. Predst. Din. Sist. Komb. i Algoritm. Metody. 12, 61–82, 244; translation in J. Math. Sci. (N. Y.) 138 (2006), no. 3, 5663–5673

Original

2006

Later among the works it cites.

A. Borodin, J. Kuan, Asymptotics of Plancherel measures for the infinite-dimensional unitary group, Adv. Math. 219 (2008) 894–931