Publications by Sergei Kerov

1974 - 1983 papers

Double function algebras on a finite group (in Russian).

Zapiski Nauchn. Seminarov LOMI, v. 39 (1974) 182-185.

English translation: J. Soviet Math., v. 8 (1997), 136-139.

Duality of finite dimensional *-algebras (in Russian).

Vestnik LGU, Math. ser., v. 7 (1974) 23-29.

Asymptotic behavior of the Plancherel measure of the symmetric group and the limit form of Young tableaux (with A.M.Vershik) (in Russian).

Dokl. Mat. Nauk, v. 233 (1977) no. 6, 1024-1027.

English translation: Soviet Math. Dokl. v. 18 (1977) 527-531.

Characters, factor-representations and K-functor of the infinite symmetric group (with A.M.Vershik) (in Russian).

Proc. Int. Conf. on Operator Algebras and Group Representations, Romania, v.1 (1980) 23-32.

Characters and factor representations of the infinite symmetric group (with A. M. Vershik) (in Russian).

Doklady AN SSSR, v. 257 (1981) no. 5 1037-1040.

English translation: Soviet Math. Dokl., v. 23 (1981) no.2, 389-392.

Asymptotic theory of characters of the symmetric group (with A.M.Vershik) (in Russian).

Funkts. Anal. i Pril., v. 15 (1981) no. 4 15-27.

English translation: Funct. Anal. and its Appl., v.15 (1981) 246-255.

Characters and factor-representations of the infinite unitary group (with A. M. Vershik) (in Russian).

Doklady AN SSSR, v. 267 (1982) no. 2, 272-276.

English translation: Soviet Math. Dokl., v. 26 (1982) no.3.

Polynomial dimension groups (in Russian).

In: Operator Theory and Function Theory, Leningrad, no.1 (1983) 185-194.

The K-functor (Grothendieck group) of the infinite symmetric group (with A. M. Vershik) (in Russian).

Zapiski Nauchn. Semin. LOMI, Leningrad, v. 123 (1983) 126-151.

English translation: J. Sov. Math., v. 28 (1985) 549-568.

W-graphs of representations of symmetric groups.

Zapiski Nauchn. Semin. LOMI, Leningrad, v. 123 (1983) 190-202

English translation: J. Sov. Math., v. 28 (1985) 596-605.

Experiments in calculating the dimensionof a typical representation of the symmetric group (with A.Vershik and A.Gribov) (in Russian).

Zapiski Nauchn. Semin. LOMI, Leningrad, v. 123 (1983) 152-154

English translation: J. Sov. Math. v. 28 (1985) 568-570.

Isomorphisms of rings constructed from simplicial schemes (with A. Karp).

Questions of differential geometry "in the large", 60--66, Leningrad. Gos. Ped. Inst., Leningrad. 1983.

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1984 - 1988 papers

The Robinson-Schensted-Knuth correspondence and the Littlewood-Richardson rule (in Russian).

Uspekhi Mat. Nauk, v. 39 (1984), no. 2, 161-162.

English translation: Russian Math. Surveys, v. 39 (1984) 165-166.

Asymptotic behavior of the maximal and generic dimensions of irreducible representations of the symmetric group (with A.Vershik) (in Russian).

Funkts. Anal. i Prilozhen. v. 19 (1985), no. 1, 25--36, 96.

English translation: Funct. Anal. and its Appl. v. 19 (1985), no.1, 21-31.

Locally semisimple algebras. Combinatorial theory and the K₀-functor (with A.Vershik) (in Russian).

Itogi Nauki, Sovr. Probl. Mat., Novejsh. Dostizh., VINITI, v. 26 (1985), 3-56.

English translation: J. Sov. Math. v. 38 (1987) 1701-1733.

The characters of the infinite symmetric groups and probability properties of the Robinson-Schensted-Knuth algorithms (with A.M.Vershik) (in Russian).

SIAM J. Alg. Discr. Meth., v. 7 (1986) 116-124.

Combinatorics, the Bethe ansatz, and representations of the symmetric group (with A.Kirillov and N.Reshetikhin, in Russian).

Zapiski Nauchn. Semin. LOMI, Leningrad, v. 155 (1986) 50-64.

English translation: J. Soviet Math., v. 41 (1988), 916-924.

Distribution of symmetry types of high rank tensors (in Russian).

Zapiski Nauchn. Semin. LOMI, Leningrad, v. 155 (1986) 181-186.

English translation: J. Soviet Math., v. 41 (1988), 995-999.

Random Young tableaux (in Russian).

Teor. Ver. i Prilozh. v. 3 (1986) 627-628.

Realizations of *-representations of Hecke algebras, and the orthogonal Young form (in Russian).

Zapiski Nauchn. Semin. LOMI, Leningrad, v. 161 (1987) 155-172.

English translation: J. Soviet Math., v. 46 (1989), 2148-215.

Realizations of representations of the Brauer semigroup (in Russian).

Zapiski Nauchn. Semin. LOMI, Leningrad, v. 164 (1987) 189-193.

English translation: J. Soviet Math., v. 47 (1989), 2503-2507.

Characters and realizations of representations of the infinite-dimensional Hecke algebra, and knot invariants (with A.Vershik) (in Russian).

Dokl. Akad. Nauk SSSR v. 301 (1988), no. 4,777--780.

English translation: Soviet Math. Dokl. v. 38 (1989), no. 1, 134--137

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1989 papers

AF-algebras of truncated Pascal triangles (with V.Volchegursky, in Russian).

In: Problems of Group Theory and Homological Algebra. Yaroslavl university, 1989, 29-37.

Combinatorial examples in the theory of AF-algebras (in Russian).

Zapiski. Nauchn. Semin. LOMI, v. 172 (1989) 55-67.

English translation: J. Soviet Math., v. 59 (1992), 1063-1071.

An algebra of invariants for the action of the group Sp(2m) on the algebra $\otimes$ M_2m C (in Russian).

Zapiski. Nauchn. Semin. LOMI, v. 172 (1989) 68-77.

English translation: J. Soviet Math., v. 59 (1992), 1072-1078.

Representations, maximal with respect to dimension, of symmetric groups (with A.Pass, in Russian).

Zapiski. Nauchn. Semin. LOMI, v. 172 (1989) 160-166.

English translation: J. Soviet Math., v. 59 (1992), 1131-1135.

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1990 papers

The Grothendieck group of the infinite symmetric group and symmetric functions (with the elements of the K₀-functor theory of AF-algebras) (with A.M.Vershik).

Adv. Stud. Contemp. Math., Gordon and Breach, v.7 (1990) 36-114.

Random processes with common cotransition probabilities (with O.Orevkova) (in Russian).

Zapiski. Nauchn. Semin. LOMI, v. 184 (1990) 169-181.

English translation: J. Math. Sciences, v. 68 (1994), 516-525.

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1991 papers

Hall-Littlewood functions and orthogonal polynomials (in Russian).

Funkts. Anal. i Prilozhen. v. 25 (1991) 78-81.

English translation: Functional Anal. Appl. 25 (1991), no. 1, 65--66

A q-analog of the hook walk algorithm for random Young tableaux.

University of Montreal, preprint CRM-1748, 1991.

Characters of Hecke and Birman-Wenzl algebras.

In: Quantum Groups, Proc. Workshops Euler Int. Math. Inst., Leningrad, USSR, Lect. Notes in Math., v.1510 (1991) 335-340.

Triangularity of transition matrices for generalized Hall-Littlewood polynomials.

In: Quantum Groups, Proc. Workshops Euler Int. Math. Inst., Leningrad, USSR, Lect. Notes in Math., v.1510 (1991) 389-390.

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1992 papers

Generalized Hall-Littlewood symmetric functions and orthogonal polynomials.

Advances in Sov. Math., v. 9 (1992) 67-94.

A q-analog of the hook walk algorithm and random Young tableaux (in Russian).

Funkts. Anal. i Prilozhen. v. 26 (1992) 35-45.

English translation: Functional Anal. Appl. 26 (1992), no. 3, 179--187.

Separation of roots of orthogonal polynomials and the limiting shape of generic large Young diagrams.

Trondheim Univ., Trondheim, Norway, Preprint no.8 (1992).

Combinatorics of rational representations of the group GL(n, C) (with A.N.Kirillov, in Russian).

Zapiski. Nauchn. Semin. POMI, v. 200 (1992) 83-90.

English translation: J. Math. Sci., v. 77 (1995), 3190-3194.

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1993 papers

Gaussian limit for the Plancherel measure of the symmetric group.

C. R. Acad. Sci. Paris, Série I, t.316 (1993) 303-308.

gZIPed PostScript

Harmonic analysis on the infinite symmetric group (with G.I.Olshanski and A.M.Vershik).

C. R. Acad. Sci. Paris, Série I, t.316 (1993) 773-778.

gZIPed PostScript

Asymptotics of the separation of roots of orthogonal polynomials (in Russian).

Algebra i Analiz, v. 5 (1993), No 5, 68-86.

English translation: St. Petersburg Math. J. v. 5 (1994), no. 5, 925--941

gZIPed PostScript

Transition probabilities of continual Young diagrams and Markov moment problem (in Russian).

Funkts. Anal. i Prilozhen., v. 27 , No 2 (1993) 32-49.

English translation: Funct. Anal. Appl. 27 (1993), no. 2, 104--117.

gZIPed PostScript

The Plancherel growth of Young diagrams and the asymptotics of interlacing sequences (in Russian).

Dokl. Akad. Nauk, v. 333 , 1 (1993) 8-10.

English translation: Russian Acad. Sci. Dokl. Math. 48 (1994), no. 3, 420--424.

The asymptotics of interlacing sequences and the growth of continual diagrams (in Russian).

Zapiski. Nauchn. Semin. POMI, v. 205 (1993) 21-29.

English translation: J. Math. Sci., v. 80 (1996), 1760-1767.

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1994 papers

Polynomial functions on the set of Young diagrams (with G.I.Olshanski)

Comptes Rend. Acad. Sci. Paris, Série I, t.319 (1994) 121-126.

Asymptotics of large random Young diagrams.

In: Abstracts of 6th Conference on Formal Power Series and Algebraic Combinatorics, DIMACS (1994) 285-294.

Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis. D. Sci. thesis (in Russian)

St. Petersburg Mathematical Society Preprints, 2001-04.

gZIPed PostScript

2003 English translation

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1995 papers

A random subdivision process generates virtual permutations with the Ewens distribution (with N.V.Tsilevich, in Russian).

Zapiski. Nauchn. Semin. POMI, v.223 (1995) 162-180.

English translation: J. Math. Sci., v. 87 (1997), 4082-4093.

Subordinators and the permutation actions with quasi-invariant measure (in Russian).

Zapiski. Nauchn. Semin. POMI, v.223 (1995) 181-218.

English translation: J. Math. Sci., v. 87 (1997), 4094-4117.

Coherent allocations, and the Ewens -- Pitman formula.

Preprint POMI 21/1995, v.21 (1995) 1-15

Small cycles of big permutations.

Preprint POMI 22/1995, v.22 (1995) 1-9

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1996 papers

A differential model for the growth of Young diagrams (in Russian).

Proceedings of the St. Petersburg Mathematical Society, v.4 (1996), 165-192.

English translation: American Mathematical Society Translations -- Series 2, v. 188 (1998)

gZIPed PostScript

The boundary of Young lattice and random Young tableaux.

In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, v.24 (1996) 133-158.

gZIPed PostScript

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1997 papers

Rook placements on Ferrers boards, and matrix integrals (in Russian).

Zapiski. Nauchn. Semin. POMI, v.240 (1997), 136-146.

PostScript

English translation: J. Math. Sci., v. 96 (1999), no.5, 3531-3536.

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1998 papers

Interlacing measures.

Amer. Math. Soc. Transl. (2) Vol.181, 1998, pp.35--83 (Advances in the Mathematical Sciences -- 35, G.I.Olshanski ed.)

(=Preprint LaBRI 1116-96 (1996) 1-53, Université de Bordeaux-I.)

Part 1 (gZIPed PostScript)

Part 2 (gZIPed PostScript)

Part 3 (gZIPed PostScript)

The boundary of the Young graph with Jack edge multiplicities (with A.Okounkov and G.Olshanskii).

Int. Math. Research Notices, 1998, No 4, p. 173--199.

(=math.QA/9703177; Preprint RIMS-1174 (1997) 1-32)

On an infinite-dimensional group over a finite field (with A.M.Vershik, in Russian)

Funkts Analiz i Prilozhen, v.32, No 3 (1998) 3-10.

English translation: Funct. Anal. Appl. 32 (1998), no. 3, 147--152 (1999).

gZIPed PostScript

The Plancherel measure of the Young-Fibonacci graph (with A.Gnedin)

Mathematical Proc. Cambridge  Philosophical  Society 129 (2000), pp. 433-446.

Preprint POMI 26/1998 pp.1-14; gZIPed PostScript

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1999 papers

The algebra of conjugacy classes in symmetric groups, and partial permutations (with V.Ivanov, in Russian).

Zapiski. Nauchn. Semin. POMI, v.256 (1999), 95-120.

English translation: J. Math. Sci. 107 (2001), no. 5, 4212-4230.

gZIPed PostScript

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2000 papers

Anisotropic Young diagrams and Jack symmetric functions.

Funkts. Analiz i Prilozh., v. 34, no. 1 (2000)

(= Preprint POMI 24/1997.)

Deposited at the archive math.CO/9712267

The Martin boundary of the Young-Fibonacci lattice (with F. Goodman).

J. Algebraic Combin. 11 (2000), no. 1, 17--48.

(= arXiv:math/9712266 [math.CO])

Equilibrium and orthogonal polynomials.

Algebra i Analiz, v. 12 (2000), no 6, 224--237.

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Posthumous Publications

• 1. Inductive-projective (IP) limit of finite groups.
• 2. The characters of the group of almost triangular matrices over a finite field.
• 3. A law of large numbers for the characters of GL_n(k).
• 4. Factor representations of the group GLB(q) associated with the infinite Grassmanian