**Advances in Soviet Mathematics**

1992;
267 pp;
Hardcover

MSC: Primary 03; 05; 20; 28; 46; 53; 58; 81;
Secondary 22; 33; 68; 70

Print ISBN: 978-0-8218-4108-2

Product Code: ADVSOV/9

List Price: $149.00

AMS Member Price: $119.20

MAA Member Price: $134.10

**Electronic ISBN: 978-1-4704-4556-0
Product Code: ADVSOV/9.E**

List Price: $149.00

AMS Member Price: $119.20

MAA Member Price: $134.10

# Representation Theory and Dynamical Systems

Share this page *Edited by *
*A. M. Vershik*

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, infinite-dimensional groups, topology, and dynamical systems. The book contains a number of useful introductory surveys; for example, one paper by Vaksman and So&ibreve;belman 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.

#### Readership

Graduate students, specialists, and mathematical physicists.

# Table of Contents

## Representation Theory and Dynamical Systems

- Cover Cover11
- Title page iii4
- Contents v6
- Editor’s Preface vii8
- Part I. Quantum Groups, Representations of Groups and Algebras 110
- On some problems in the theory of quantum groups 312
- Representations of quantum *-algebras 𝑠𝑙_{𝑡}(𝑁+1,ℝ) 5766
- Generalized Hall-Littlewood symmetric functions and orthogonal polynomials 6776
- Formulation of Bell type problems and “noncommutative” convex geometry 95104
- Projective representations of the infinite symmetric group 115124
- Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation 131140
- Relations between compact quantum groups and Kac algebras 151160
- Combinatorial complexity of orbits in representations of the symmetric group 161170
- Part II. Dynamical Systems and Approximations 183192
- Adic models of ergodic transformations, spectral theory, substitutions, and related topics 185194
- Periodic metrics 205214
- Flows with positive entropy 211220
- On the spectral theory of adic transformations 217226
- On simultaneous action of Markov shift and adic transformation 231240
- About a certain weakly mixing substitution 241250
- Manifolds with intrinsic metric, and nonholonomic spaces 253262
- Back Cover Back Cover1278