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Hardcover ISBN:  9780821841082 
Product Code:  ADVSOV/9 
List Price:  $157.00 
MAA Member Price:  $141.30 
AMS Member Price:  $125.60 
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Product Code:  ADVSOV/9.E 
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AMS Member Price:  $125.60 
Hardcover ISBN:  9780821841082 
eBook ISBN:  9781470445560 
Product Code:  ADVSOV/9.B 
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Book DetailsAdvances in Soviet MathematicsVolume: 9; 1992; 267 ppMSC: Primary 03; 05; 20; 28; 46; 53; 58; 81
This volume presents research conducted between 1989 and 1991 by the participants in the Leningrad Seminar on representation theory, dynamical systems, and their applications, headed by A. M. Vershik. The primary areas covered here are mathematical physics, Lie groups and their representations, infinitedimensional groups, topology, and dynamical systems. The book contains a number of useful introductory surveys; for example, one paper by Vaksman and Soĭbelman provides a systematic description of the theory of quantum groups in the spirit of representation theory—a new and popular area for which there are few introductory surveys. A portion of the book is devoted to adic transformations and substitutions, a new area of ergodic theory. With a balance of survey papers and frontier research results, this book will appeal to graduate students and researchers alike.
ReadershipGraduate students, specialists, and mathematical physicists.

Table of Contents

Part I. Quantum Groups, Representations of Groups and Algebras [ MR MR1166193 ]

Ya. Soibelman and L. Vaksman — On some problems in the theory of quantum groups

E. Vaysleb — Representations of quantum $*$algebras $sl_t(N+1,\Bbb R)$

S. Kerov — Generalized HallLittlewood symmetric functions and orthogonal polynomials

A. Vershik and B. Tsirelson — Formulation of Bell type problems and “noncommutative” convex geometry

M. Nazarov — Projective representations of the infinite symmetric group

V. Ostrovskii and Yu. Samoilenko — Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation

L. Vainerman — Relations between compact quantum groups and Kac algebras

A. Barvinok — Combinatorial complexity of orbits in representations of the symmetric group

Part II. Dynamical Systems and Approximations [ MR MR1166193 ]

A. Vershik and A. Livshits — Adic models of ergodic transformations, spectral theory, substitutions, and related topics

D. Burago — Periodic metrics

D. Burago — Flows with positive entropy

B. Solomyak — On the spectral theory of adic transformations

M. Solomyak — On simultaneous action of Markov shift and adic transformation

A. Livshits — About a certain weakly mixing substitution

V. Berestovskii and A. Vershik — Manifolds with intrinsic metric, and nonholonomic spaces


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This volume presents research conducted between 1989 and 1991 by the participants in the Leningrad Seminar on representation theory, dynamical systems, and their applications, headed by A. M. Vershik. The primary areas covered here are mathematical physics, Lie groups and their representations, infinitedimensional groups, topology, and dynamical systems. The book contains a number of useful introductory surveys; for example, one paper by Vaksman and Soĭbelman provides a systematic description of the theory of quantum groups in the spirit of representation theory—a new and popular area for which there are few introductory surveys. A portion of the book is devoted to adic transformations and substitutions, a new area of ergodic theory. With a balance of survey papers and frontier research results, this book will appeal to graduate students and researchers alike.
Graduate students, specialists, and mathematical physicists.

Part I. Quantum Groups, Representations of Groups and Algebras [ MR MR1166193 ]

Ya. Soibelman and L. Vaksman — On some problems in the theory of quantum groups

E. Vaysleb — Representations of quantum $*$algebras $sl_t(N+1,\Bbb R)$

S. Kerov — Generalized HallLittlewood symmetric functions and orthogonal polynomials

A. Vershik and B. Tsirelson — Formulation of Bell type problems and “noncommutative” convex geometry

M. Nazarov — Projective representations of the infinite symmetric group

V. Ostrovskii and Yu. Samoilenko — Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation

L. Vainerman — Relations between compact quantum groups and Kac algebras

A. Barvinok — Combinatorial complexity of orbits in representations of the symmetric group

Part II. Dynamical Systems and Approximations [ MR MR1166193 ]

A. Vershik and A. Livshits — Adic models of ergodic transformations, spectral theory, substitutions, and related topics

D. Burago — Periodic metrics

D. Burago — Flows with positive entropy

B. Solomyak — On the spectral theory of adic transformations

M. Solomyak — On simultaneous action of Markov shift and adic transformation

A. Livshits — About a certain weakly mixing substitution

V. Berestovskii and A. Vershik — Manifolds with intrinsic metric, and nonholonomic spaces