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Neretin Yurii Aleksandrovich

Statistics Math-Net.Ru
Total publications: 68
Scientific articles: 59
Presentations: 14

Number of views:
This page:5141
Abstract pages:16397
Full texts:4206
References:1964
Professor
Doctor of physico-mathematical sciences (1992)
Birth date: 2.07.1959
E-mail: ,
Website: http://wwwth.itep.ru/~neretin, http://www.mat.univie.ac.at/~neretin
Keywords: representation theory, infinite-dimensional groups, analysis on homogeneous spaces, symmetric spaces, analysis of matrix variable.spectral curve, elliptic curves, free group, line bundles.
UDC: 512.54, 512.546, 512.625.5, 512.64, 512.741.5, 512.763, 512.772, 512.816.3, 512.816.4, 514.7, 514.76, 517.4, 517.444, 517.53, 517.57, 517.587, 517.588, 517.98, 517.986, 517.986.6, 517.987.1, 519.21, 519.4, 519.46
MSC: 22Exx, 43A85, 53C35, 33Dxx, 60G99, 17Bxx

Subject:

Infinite dimensional groups, classical groups, special functions, symmetric spaces, operator theory, mathematical physics.

   
Main publications:
  • Neretin Yu. A. Categories of symmetries and infinite-dimensional groups. London Mathematical Society Monographs. New Series, 16. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1996. xiv+417 pp.; Russian variant: URSS, 1998.
  • Neretin Yu. A. Representations of Virasoro algebra and affine algebras // Current problems in mathematics. Fundamental directions, vol. 22 (Russian), 163–224; Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1988. English transl.: Representation theory and noncommutative harmonic analysis. I, 157–234; Encyclopaedia Math. Sci., 22, Springer, Berlin, 1994.
  • Neretin Yu. A. Almost invariant structures and constructions of unitary representations of the group of diffeomorphisms of the circle // Dokl. Akad. Nauk SSSR 294 (1987), no. 1, 37–41. English transl.: Soviet Math. Dokl. 35 (1987), no. 3, 500–504.
  • Neretin Yu. A. Holomorphic continuations of representations of the group of diffeomorphisms of the circle // Mat. Sb. 180 (1989), no. 5, 635–657, 720.
  • Neretin Yu. A. Plancherel formula for Berezin deformation of $L^2$ on Riemannian symmetric space. Preprint, available via http://www.arXiv.org/math.RT/9911020.

http://www.mathnet.ru/eng/person8444
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/210026

Publications in Math-Net.Ru
1. Operational calculus for Fourier transform on the group $\operatorname{GL}(2,\mathbb{R})$ and problem about action of overalgabra in Plancherel decomposition
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 52:3 (2018),  42–52
2. Infinite symmetric group, pseudomanifolds, and combinatorial cobordism-like structures
Alexander A. Gaifullin, Yury A. Neretin
J. Topol. Anal., 10:3 (2018),  605–625
3. On the group of infinite $p$-adic matrices with integer elements
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 468 (2018),  105–125
4. Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 51:2 (2017),  25–41
5. Combinatorial encodings of infinite symmetric groups and descriptions of semigroups of double cosets
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 462 (2017),  65–92
6. On the Sphericity of the Subgroup $\operatorname{PSL}_2(\mathbb{R})$ in the Group of Diffeomorphisms of the Circle
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 50:2 (2016),  91–94
7. Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions
Yu. A. Neretin
Izv. RAN. Ser. Mat., 80:6 (2016),  127–140
8. Wishart–Pickrell distributions and closures of group actions
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 448 (2016),  236–245
9. Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat–Tits buildings
Yu. A. Neretin
Izv. RAN. Ser. Mat., 79:3 (2015),  87–130
10. Infinite symmetric groups and combinatorial constructions of topological field theory type
Yu. A. Neretin
Uspekhi Mat. Nauk, 70:4(424) (2015),  143–204
11. Several remarks on groups of automorphisms of free groups
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 436 (2015),  189–198
12. Bi-invariant functions on the group of transformations leaving a measure quasi-invariant
Yu. A. Neretin
Mat. Sb., 205:9 (2014),  145–160
13. On an infinite-dimensional limit of the Steinberg representations
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 421 (2014),  126–132
14. Hua measures on the space of $p$-adic matrices and inverse limits of Grassmannians
Yu. A. Neretin
Izv. RAN. Ser. Mat., 77:5 (2013),  95–108
15. On the boundary of the group of transformations leaving a measure quasi-invariant
Yu. A. Neretin
Mat. Sb., 204:8 (2013),  83–116
16. On topologies on Malcev completions of braid groups
Yury Neretin
Mosc. Math. J., 12:4 (2012),  803–824
17. A remark on representations of infinite symmetric groups
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 403 (2012),  103–109
18. Sphericity and multiplication of double cosets for infinite-dimensional classical groups
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 45:3 (2011),  79–96
19. Spectral data for a pair of matrices of order three and an action of the group $\mathrm{GL}(2,\mathbb Z)$
Yu. A. Neretin
Izv. RAN. Ser. Mat., 75:5 (2011),  93–102
20. On Spherical Functions on the Group $\operatorname{SU}\times\operatorname{SU}\times\operatorname{SU}$
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 44:1 (2010),  59–67
21. On the beta function of the tube of the light cone
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 378 (2010),  73–80
22. $K$-Finite Matrix Elements of Irreducible Harish-Chandra Modules are Hypergeometric
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 41:4 (2007),  60–69
23. Perelomov Problem and Inversion of the Segal–Bargmann Transform
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 40:4 (2006),  104–107
24. Central extensions of groups of symplectomorphisms
Yu. A. Neretin
Mosc. Math. J., 6:4 (2006),  703–729
25. Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems
Yu. A. Neretin
Mat. Sb., 197:11 (2006),  51–78
26. Notes on Stein–Sahi representations and some problems of non-$L^2$-harmonic analysis
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 331 (2006),  125–169
27. Some Continuous Analogs of the Expansion in Jacobi Polynomials and Vector-Valued Orthogonal Bases
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 39:2 (2005),  31–46
28. On compression of Bruhat–Tits buildings
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 325 (2005),  163–170
29. Beta functions of Bruhat–Tits buildings and deformation of $l^2$ on the set of $p$-adic lattices
Yu. A. Neretin
Mat. Sb., 194:12 (2003),  31–62
30. Rayleigh triangles and non-matrix interpolation of matrix beta integrals
Yu. A. Neretin
Mat. Sb., 194:4 (2003),  49–74
31. The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction
Yu. A. Neretin
Izv. RAN. Ser. Mat., 66:5 (2002),  171–182
32. Beta-integrals and finite orthogonal systems of Wilson polynomials
Yu. A. Neretin
Mat. Sb., 193:7 (2002),  131–148
33. Spreading maps (polymorphisms), symmetries of Poisson processes, and matching summation
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 292 (2002),  62–91
34. Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants
Yu. A. Neretin
Mosc. Math. J., 1:2 (2001),  157–220
35. Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces
Yu. A. Neretin
Mat. Sb., 192:3 (2001),  83–114
36. On the Separation of Spectra in the Analysis of Berezin Kernels
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 34:3 (2000),  49–62
37. Matrix analogues of the beta function and Plancherel's formula for Berezin kernel representations
Yu. A. Neretin
Mat. Sb., 191:5 (2000),  67–100
38. Conformal geometry of symmetric spaces and generalized linear-fractional maps of Krein–Shmul'yan
Yu. A. Neretin
Mat. Sb., 190:2 (1999),  93–122
39. Pseudo-Riemannian symmetric spaces: uniform realizations, and open embeddings into Grassmanians
Yu. A. Neretin
Zap. Nauchn. Sem. POMI, 256 (1999),  145–167
40. Supercomplete Bases in the Space of Symmetric Functions
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 32:1 (1998),  12–28
41. The restrictions of functions holomorphic in a domain to curves lying on its boundary, and discrete $\operatorname{SL}_2(\mathbb R)$-spectra
Yu. A. Neretin
Izv. RAN. Ser. Mat., 62:3 (1998),  67–86
42. Hausdorff Metric, the Construction of a Hausdorff Quotient Space, and Boundaries of Symmetric Spaces
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 31:1 (1997),  83–86
43. On the correspondence between boson Fock space and the $L^2$ space with respect to Poisson measure
Yu. A. Neretin
Mat. Sb., 188:11 (1997),  19–50
44. Fractional diffusions and quasi-invariant actions of infinite-dimensional groups
Yu. A. Neretin
Tr. Mat. Inst. Steklova, 217 (1997),  135–181
45. The group of diffeomorphisms of the half-line, and random Cantor sets
Yu. A. Neretin
Mat. Sb., 187:6 (1996),  73–84
46. Boundary values of holomorphic functions, singular unitary representations of $O(p,q)$, and their limits as $q\to\infty$
Yu. A. Neretin, G. I. Ol'shanski
Zap. Nauchn. Sem. POMI, 223 (1995),  9–91
47. Universal completions of complex classical groups
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 26:4 (1992),  30–44
48. On combinatorial analogs of the group of diffeomorphisms of the circle
Yu. A. Neretin
Izv. RAN. Ser. Mat., 56:5 (1992),  1072–1085
49. Categories of bistochastic measures, and representations of some infinite-dimensional groups
Yu. A. Neretin
Mat. Sb., 183:2 (1992),  52–76
50. Extension of representations of classical groups to representations of categories
Yu. A. Neretin
Algebra i Analiz, 3:1 (1991),  176–202
51. A semigroup of operators in the boson fock space
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 24:2 (1990),  63–73
52. A spinor representation of an infinite-dimensional orthogonal semigroup and the virasoro algebra
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 23:3 (1989),  32–44
53. Holomorphic extensions of representations of the group of the diffeomorphisms of the circle
Yu. A. Neretin
Mat. Sb., 180:5 (1989),  635–657
54. Representations of Virasoro algebra and affine algebras
Yu. A. Neretin
Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 22 (1988),  163–224
55. A complex semigroup that contains the group of diffeomorphisms of the circle
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 21:2 (1987),  82–83
56. An estimate of the number of parameters defining an $n$-dimensional algebra
Yu. A. Neretin
Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987),  306–318
57. Representations of complementary series entering discretely in tensor products of unitary representations
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 20:1 (1986),  79–80
58. Unitary representations of the diffeomorphism group of the $p$-adic projective line
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 18:4 (1984),  92–93
59. Unitary representations with highest weight of the group of diffeomorphisms of a circle
Yu. A. Neretin
Funktsional. Anal. i Prilozhen., 17:3 (1983),  85–86
60. The complementary series of representations of the group of diffeomorphisms of the circle
Yu. A. Neretin
Uspekhi Mat. Nauk, 37:2(224) (1982),  213–214
61. Differential operators on Lie groups
Yu. A. Neretin
Uspekhi Mat. Nauk, 36:2(218) (1981),  195–196

62. Unified State Exam and agony of school mathematics
Yu. A. Neretin
Math. Ed., 2016, no. 4(80),  2–14
63. Vladimir Fedorovich Molchanov (on his 75th birthday)
S. G. Gindikin, R. S. Ismagilov, A. V. Karabegov, Yu. A. Neretin, N. I. Nessonov, G. I. Ol'shanski
Uspekhi Mat. Nauk, 69:3(417) (2014),  186–190
64. Rais Sal'manovich Ismagilov (on his 75th birthday)
A. M. Vershik, A. A. Kirillov, V. F. Molchanov, Yu. A. Neretin, G. I. Olshanski, V. V. Ryzhikov, V. M. Tikhomirov, A. A. Shkalikov
Uspekhi Mat. Nauk, 68:4(412) (2013),  185–190
65. Sabir Medgidovich Gusein-Zade
S. B. Artemov, A. A. Belavin, V. M. Buchstaber, A. I. Esterov, B. L. Feigin, V. A. Ginzburg, E. A. Gorsky, Yu. S. Ilyashenko, A. A. Kirillov, A. G. Khovanskii, S. K. Lando, G. A. Margulis, Yu. A. Neretin, S. P. Novikov, S. B. Shlosman, A. B. Sossinsky, M. A. Tsfasman, A. N. Varchenko, V. A. Vassiliev, S. G. Vlăduţ
Mosc. Math. J., 10:4 (2010),  831–832
66. Entrance Examination Patience: Russia and the West
Yu. A. Neretin
Math. Ed., 2009, no. 2(50),  3–13
67. Mathematical works of D. P. Zhelobenko
Yu. A. Neretin, S. M. Khoroshkin
Uspekhi Mat. Nauk, 64:1(385) (2009),  178–188
68. Mark Iosifovich Graev (to his 85th brithday)
A. M. Vershik, I. M. Gel'fand, S. G. Gindikin, A. A. Kirillov, G. L. Litvinov, V. F. Molchanov, Yu. A. Neretin, V. S. Retakh
Uspekhi Mat. Nauk, 63:1(379) (2008),  169–182
69. Education and "Snowball" Technology
Yu. A. Neretin
Math. Ed., 2007, no. 1(41),  45–48
70. Improbable Coincidences and the Morozov–Fomenko Problem on Historical Foldings
Yu. A. Neretin
Math. Ed., 2002, no. 2(21),  66–95

Presentations in Math-Net.Ru
1. Двойные классы смежности на бесконечномерных классических группах и рациональные отображения грассманианов
Yu. A. Neretin

September 6, 2018 18:30   
2. Гауссовские меры и размазывающие отображения
Yu. A. Neretin
Dynamical systems and differential equations
April 19, 2018 16:45
3. Higher dimensional analogs of Livshits–Potapov characteristic functions and inner functions of a matrix variable
Yu. A. Neretin
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
April 19, 2017 16:45
4. Детерминантные процессы и фермионные гауссовы операторы
Yu. A. Neretin
Dynamical systems and differential equations
April 17, 2017 18:30
5. Closures of group actions and Poisson measures
Yury Neretin
International Conference “Anosov Systems and Modern Dynamics” dedicated to the 80th anniversary of Dmitry Anosov
December 19, 2016 12:10   
6. Инварианты классов сопряженных элементов и рациональные отображения грассманианов
Yu. A. Neretin
Annual memorial conference dedicated to the memory of Andrei Nikolaevich Tyurin
October 28, 2013 15:00   
7. Infinite symmetric group, two-dimensional simplicial bordisms, and Feynman diagrams
Yu. A. Neretin
Globus Seminar
December 13, 2012 15:40   
8. Спектральные данные для многих матриц и умножение двойных классов смежности на бесконечномерных группах
Yu. A. Neretin
Weekly seminar of Laboratory of algebraic geometry
February 24, 2012 17:00
9. Представления бесконечной симметрической группы и топологические теории поля
Yurii Neretin
Homology and homotopy methods in geometry
March 24, 2010
10. Представления бесконечной симметрической группы и топологические теории поля
Yu. A. Neretin
Seminar of the Department of Algebra
November 17, 2009 15:00
11. Бесконечномерные классические группы и рациональные кривые в лагранжевом грассманиане
Yu. A. Neretin
Seminar of the Department of Algebra
March 24, 2009 15:00
12. Ортосимплектические спиноры и лаграгжев супер-грассманиан
Yu. A. Neretin
Seminar of the Department of Algebra
October 14, 2008 15:00
13. О сферических функциях на группе $\mathrm{SU}(2)\times\mathrm{SU}(2)\times\mathrm{SU}(2)$
Yu. A. Neretin
Lie groups and invariant theory
April 2, 2008
14. Ветвящиеся интегралы и области голоморфности матричных элементов полупростых групп
Yu. A. Neretin
Seminar on Geometry of Algebraic Varieties
December 24, 2007 14:00

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