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
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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.
|