G. Olshanski - Publications

2010

Gnedin A., Olshanski G., q-Exchangeability via quasi-invariance, Annals of Probability 38 (2010), Number 6, 2103-2135; arXiv:0907.3275. http://arxiv.org/abs/arXiv:0907.3275
Olshanski G., Plancherel averages: Remarks on a paper by Stanley, Electronic Journal of Combinatorics 17 (2010), paper #R43; arXiv:0905.1304. http://arxiv.org/abs/0905.1304

2009

Olshanski G., Plancherel averages: Remarks on a paper by Stanley, arXiv:0905.1304. http://arxiv.org/abs/0905.1304
Gnedin A., Olshanski G., q-Exchangeability via quasi-invariance, arXiv:0907.3275. http://arxiv.org/abs/0907.3275
Olshanski G., The quasi-invariance property for the Gamma kernel determinantal measure, arXiv:0910.0130. http://arxiv.org/abs/0910.0130
Olshanski G., Anisotropic Young Diagrams and Infinite-Dimensional Diffusion Processes with the Jack Parameter. International Mathematics Research Notices 2009; online publication: doi: 10.1093/imrn/rnp168.
Borodin A.M., Olshanski G., Infinite-dimensional diffusions as limits of random walks on partitions. Probability Theory and Related Fields 144 (2009), no. 1, 281--318.
Gnedin A., Olshanski G., A q-analogue of de Finetti"s theorem, Electronic Journal of Combinatorics 16 (2009), no. 1, paper #R78

2008

Olshanski G., Difference operators and determinantal point processes, Functional Analysis and its Applications 42 (2008), no. 4, 317--329

2007

Borodin A., Olshanski G., Asymptotics of Plancherel--type random partitions. Journal of Algebra, 313 (2007), no. 1, 40--60.

2006

Borodin A., Olshanski G., Markov processes on partitions, Probability Theory and Related Fields, 135 (2006), no. 1, 84--152.
Olshanski G., Okounkov A., Limits of BC--type orthogonal polynomials as the number of variables goes to infinity, In: Jack, Hall--Littlewood and Macdonald polynomials, American Mathematical Society Contemporary Mathematics Series 417 (2006), 281--318.
Borodin A., Olshanski G., Stochastic dynamics related to Plancherel measure on partitions, In: Representation Theory, Dynamical Systems, and Asymptotic Combinatorics. American Mathematica Society Translations--Series 2: Advances in the Mathematical Sciences, vol. 217, 2006, 9--21.
Gnedin A., Olshanski G., The boundary of the Eulerian number triangle. Moscow Mathematical Journal 6 (2006), no. 3, 461--475.
Borodin F., Olshanski G., Meixner polynomials and random partitions. Moscow Mathematical Journal 6 (2006), no. 4, 629--655.

2005

Borodin A., Olshanski G., Harmonic analysis on the infinite--dimensional unitary group and determinantal point processes. Annals of Mathematics 161 (2005), no.3, 1319--1422.
Borodin A., Olshanski G., Z-measures on partitions and their scaling limits. European Journal of Combinatorics 26 (2005), no. 6, 795--834.
Borodin A., Olshanski G., Random partitions and the Gamma kernel. Advances in Mathematics, 194 (2005), no. 1, 141--202.
Borodin A., Olshanski G., Representation theory and random point processes, In: European congress of mathematics (ECM), Stockholm, Sweden, June 27--July 2, 2004. Z"urich: European Mathematical Society, 2005, pp. 73--94.

2004

Kerov S., Olshanski G., Vershik A., Harmonic analysis on the infinite symmetric group. Inventiones Mathematicae 158 (2004), no. 3, 551--642.

2003

Olshanski G., Regev A., Vershik A., Frobenius--Schur functions. In: Studies in Memory of Issai Schur. Progress in Mathematics 210, Birkh"auser, 2003, pp. 251--300.
Olshanski G., Point processes related to the infinite symmetric group. In: The orbit method in geometry and physics: in honor of A.A. Kirillov. Progress in Mathematics 213, Birkh"auser, 2003, pp. 349--393.
Olshanski G., An introduction to harmonic analysis on the infinite symmetric group. In: Asymptotic Combinatorics with Applications to Mathematical Physics (A. Vershik, ed.). Springer Lecture Notes in Math. 1815, 2003, 127--160.
Olshanski G., The problem of harmonic analysis on the infinite-dimensional unitary group. Journal of Functional Analysis 205 (2003), no. 2, pp. 464--524.
Olshanski G., Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities. Functional Analysis and its Applications 37 (2003), 281--301.

2002

Ivanov V., Olshanski G., Kerov"s central limit theorem for the Plancherel measure on Young diagrams. In: Symmetric functions 2001. Surveys of developments and perspectives. Kluwer, 2002, pp. 93--151.

2001

Molev A., Olshanski G., Degenerate affine Hecke algebras and centralizer construction for the symmetric groups. Journal of Algebra 237 (2001), 302--341.
Borodin A., Olshanski G., Z-Measures on partitions, Robinson--Schensted--Knuth correspondence, and beta=2 ensembles. In: Random matrix models and their applications. MSRI Publications, vol. 40, Cambridge Univ. Press, 2001, 71--94.
Olshanski G., Regev A., Random Young tableaux and combinatorial identities. Seminaire Lotharingien de Combinatoire 46 (2001), paper B46e (30 pp).
Borodin A., Olshanski G., Infinite random matrices and ergodic measures. Communications in Mathematical Physics 223 (2001), no. 1, 87--123.

2000

Borodin A., Olshanski G., Distributions on partitions, point processes, and the hypergeometric kernel, Communications in Mathematical Physics 211 (2000), no. 2, 335--358.
Borodin A., Okounkov A., Olshanski G., Asymptotics of Plancherel measures for symmetric groups, J. American Mathematical Society 13 (2000), no. 3, 481--515.
Molev A., Olshanski G., Centralizer construction for twisted Yangians, Selecta Mathematica 6 (2000), no. 3, 269--317.
Borodin A., Olshanski G., Harmonic functions on multiplicative graphs and interpolation polynomials. Electronic Journal of Combinatorics 7 (2000), paper #R28.

1998

Okounkov A., Olshanski G., Shifted Schur functions II. The binomial formula for characters of classical groups and its applications, in: Kirillov"s Seminar on Representation Theory. American Mathematica Society Translations, 1998, 245--271.
Kerov S., Okounkov A., Olshanski G., The boundary of Young graph with Jack edge multiplicities, International Mathematics Research Notices, 1998, no. 4, 173--199.
Okounkov A., Olshanski G., Asymptotics of Jack polynomials as the number of variables goes to infinity, International Mathematics Research Notices 1998, no. 13, 641--682.
Borodin A., Olshanski G., Point processes and the infinite symmetric group, Mathematical Research Letters 5 (1998), 799--816.

1997

Okounkov A., Olshanski G., Shifted Schur functions, Algebra i Analiz 9 (1997), no. 2, 73--146 (Russian); English version: St. Petersburg Mathematical Journal 9 (1998), 239--300.
Olshanski G., Generalized symmetrization in enveloping algebras, Transformation Groups 2 (1997), 197--213.
Okounkov A., Olshanski G., Shifted Jack polynomials, binomial formula, and applications, Mathematical Research Letters 4 (1997), 69--78.

1996

Molev A., Nazarov M., Olshanski G., Yangians and classical Lie algebras. Russian Mathematical Surveys 51, no. 2 (1996), 205-282.
Olshanski G., Vershik A., Ergodic unitarily invariant measures on the space of infinite Hermitian matrices, in: Contemporary Mathematical Physics. F.A..Berezin"s memorial volume. American Mathematical Society Translations, Series 2, Vol. 175 (Advances in the Mathematical Sciences --- 31), 1996, pp. 137--175.
Nazarov M., Olshanski G., Bethe subalgebras in twisted Yangians, Communications in Mathematical Physics 178 (1996), 483-506.

1995

Olshanski G., Cauchy--Szeg"o kernels for Hardy spaces on simple Lie groups, Journal of Lie Theory, 5 (1995), 241--273.
Neretin Yu., Olshanski G., Boundary values of holomorphic functions, singular unitary representations of the groups O(p,q), and their limits as q--> infty. Zapiski POMI 223 (1995), 9-91 (Russian); English translation: Journal of Mathematical Sciences (New York) 87 (1997), no. 6, 3983-4035.

1994

Olshanski G., Weil representation and norms of Gaussian operators. Functional Analysis and its Applications 28 (1994), 42--54.
Kerov S., Olshanski G., Polynomial functions on the set of Young diagrams, Comptes Rendus Acad. Sci. Paris, Ser. I, 319 (1994), 121--126.

1993

Kerov S., Olshanski G., Vershik A., Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. Comptes Rendus de l"Academie des Sciences Paris. Ser. 1, 316 (1993), 773-778.

1992

Olshanski G., Twisted Yangians and infinite-dimensional classical Lie algebras. In: Lecture Notes in Mathematics 1510 (1992), 103--120.
Olshanski G., Quantized universal enveloping superalgebra of type Q and a super-extension of the Hecke algebra. Letters in Mathematical Physics 24 (1992), 93-102.

1991

Olshanski G., Representations of infinite-dimensional classical groups, limits of enveloping algebras, and Yangians. In: Topics in Representation Theory. Advances in Soviet Mathematics, vol. 2. American Mathematical Society, Providence, R.I., 1991, 1-66.
Olshanski G., On semigroups related to infinite-dimensional groups. In: Topics in representation theory. Advances in Soviet Mathematics., vol. 2. American Mathematical Society Providence, R.I., 1991, 67-101.
Olshanski G., Caract`eres generalis"es du groupe U(infty) et fonctions interieures. Comptes Rendus de l"Academie des Sciences Paris. Ser. 1, 313 (1991), 9--12.

1990

Olshanski G., Unitary representations of infinite-dimensional pairs (G,K) and the formalism of R. Howe. In: Representations of Lie groups and related topics. Advances in Contemporary Mathematics, vol. 7 (A.M. Vershik and D.P. Zhelobenko, editors). Gordon and Breach, N.Y., London etc. 1990, 269--463.

1989

Olshanski G., Irreducible unitary representations of the groups U(p,q) sustaining passage to the limit as q-->infty. Zapiski Nauchnyh Seminrov LOMI, vol. 172 (1989), 114-120 (Russian); English translation: Journal of Soviet Mathematics [currently Journal of Mathematical Scinces (New York)] 59, no. 5 (1992), 1102-1107.
Olshanski G., Unitary representations of (G,K)-pairs connected with the infinite symmetric group S(infty). Leningrad [currently St.Petersburg] Mathematical Journal 1, no. 4 (1990), 983--1014. [Translation from Algebra i Analiz, 1:4, 1989]
Nazarov M., Neretin Yu., Olshanski G., Semi-groupes engendr"es par la repr"esentation de Weil du groupe symplectique de dimension infinie. Comptes Rendus de l"Academie des Sciences Paris. Ser. 1, 309, no. 7 (1989), 443--446.

1988

Olshanski G., Determinism of L"evy random fields and unitary representations of infinite-dimensional groups. Russian Math. Surveys 43, no. 2 (1988), 183-184.
Olshanski G., Method of holomorphic extensions in the representation theory of infinite-dimensional classical groups. Funct. Anal. Appl. 22, no. 4 (1989), 273-285 [Russian original: 1988]

1987

Olshanski G., Yangians and universal enveloping algebras. Zapiski Nauchnyh Seminarov LOMI, vol. 164 (1987), 142-150 (Russian); English translation: Journal of Soviet Mathematics [currently Journal of Mathematical Science (New York)] 47, no. 2 (1989), 2466-2473.
Olshanski G., Extension of the algebra U(g) for infinite-dimensional classical Lie algebras g, and the Yangians Y(gl(m)). Soviet Math. Dokl. 36, no. 3 (1988), 569-573. Translation from Dokl. Akad. Nauk SSSR 297, 1050-1054 (1987)

1986

Olshanski G., Unitary representations of the group SO(infty,infty) as limits of unitary representations of the groups SO(n,infty) as n --> infty. Functional Analysis and its Applications 20, no. 4 (1987), 292-301. [Russian original: 1986]

1985

Olshanski G., Prati M.C., Extremal weights of finite-dimensional representations of the Lie superalgebra gl_{n/m}. Il Nuovo Cimento 85A, no. 1 (1985), 1-18.
Olshanski G., Unitary representations of the infinite symmetric group: a semigroup approach. In: Representations of Lie groups and Lie algebras (A.A. Kirillov, ed.). Budapest, Akad. Kiado, 1985, 181-198.

1984

Olshanski G., Infinite-dimensional classical groups of finite R-rank: description of representations and asymptotic theory. Functional Analysis and its Applications 18, no. 1 (1984), 22-34.

1983

Olshanski G., Unitary representations of infinite-dimensional pairs (G,K) and the formalism of R. Howe. Soviet Mathematics Doklady 27, no. 2 (1983), 290-294.

1982

Olshanski G., Invariant orderings in simple Lie groups: the solution to E.B.Vinberg"s problem. Funct. Anal. Appl. 16 (1983), 80-81. [Russian rginal: 1982].
Olshanski G., Convex cones in symmetric Lie algebras, Lie semigroups, and invariant causal (order) structures on pseudo-Riemannian symmetric spaces. Soviet Math. Dokl. 26 (1982), 97-101.
Olshanski G., Complex Lie semigroups, Hardy spaces, and the Gelfand- Gindikin program. In: Topics in group theory and homological algebra. Yaroslavl University Press, 1982, 85-98 (Russian). English translation: Differential Geometry and its Applications, 1 (1991),297-308.
Olshanski G., Spherical functions and characters on the group U(infty)^X. Russian Mathematical Surveys 37, no. 2 (1982), 233-234.

1981

Olshanski G., Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series. Funct. Anal. Appl. 15 (1982), 275-285. [Russian original: 1981]

1980

Olshanski G., Construction of unitary representations of infinite-dimensional classical groups. Soviet Math. Doklady 21 (1980), 66-70.
Olshanski G., Description of unitary representations with highest weight for the groups $U(p,q)^{sim}$. Funct. Anal. Appl. 14 (1981), 190-200. [Russian original: 1980]
Olshanski G., New ``large"" groups of type one. Journal of Soviet Mathematics [currently Journal of Mathematical Science (New York)] 18 (1982), 22-39. [Russian original: 1980]

1978

Olshanski G., Unitary representations of the infinite--dimensional classical groups $U(p,infty)$, $SO(p,infty)$, $Sp(p, infty)$ and the corresponding motion groups. Soviet Math. Doklady 19 (1978), 220-224.
Olshanski G., Unitary representations of the infinite--dimensional classical groups $U(p,infty)$, $SO(p,infty)$, $Sp(p, infty)$ and the corresponding motion groups. Funct. Anal. Appl. 12 (1979), 185-195. [Russian original: 1978]

1977

Olshanski G., Classification of irreducible representations of groups of automorphisms of Bruhat--Tits trees. Funct. Anal. Appl. 11, no. 1 (1977), 26-34.

1975

Olshanski G., On representations of the group of automorphisms of a tree. Uspehi Mat. Nauk. 30, no. 3 (1975), 169-170 (Russian).

1974

Olshanski G., Intertwining operators and complementary series in the class of representations of the general linear group over a locally compact division algebra induced from parabolic subgroups. Math. USSR--Sbornik 22 (1974), 217--255.

1973

Olshanski G., On unitary representations of the groups $GL(2)$ and $GU(2)$ over a totally disconnected locally compact quaternion field. Funct. Anal. Appl. 7, no. 1 (1973), 73-75.

1972

Olshanski G., On intertwining operators for induced representations of reductive $p$-adic groups. Russian Math. Surveys 27, no. 6 (1972), 243-244.

1969

Olshanski G., Topology of the space of unitary representations of a nilpotent Lie group. Funct. Anal. Appl. 3, no. 4 (1969), 340-342.
Olshanski G., On the Frobenius reciprocity theorem. Funct. Anal. Appl. 3, no. 4 (1969), 295-302.