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 Solbelman 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.
Table of contents:
Part I.Quantum Groups, Representations of Groups and Algebras Ya. S. Solbelman and L. L. Vaksman: On some problems in the theory of quantum groups; E. Ye. Vaysleb: Representations of quantum *-algebras slt(N + 1, R) ; S. V. Kerov: Generalized Hall-Littlewood symmetric functions and orthogonal polynomials; A. M. Vershik and B. S. Tsirelson: Formulation of Bell type problems and "noncommutative" convex geometry; M. L. Nazarov: Projective representations of the infinite syummetric group; V. L. Ostrovskii and Yyu. S. Samollenko: Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation; L. I. Valnerman: Relations between compact quantum groups and Kac algebras; A. I. Barvinok: Combinatorial complexity of orbits in representations of the symmetric group; Part II. Dynamical Systems and Approximations A. M. Vershik and A. N. Livshits: Adic models of ergodic transformations, spectral theory, substitutions, and related topics; D. Yu. Burago: Periodic metrics; D. Yu. 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. N. Livshits: About a certain weakly mixing substitution; Vn N. Berestovskii and A. M. Vershik: Manifolds with intrinsic metric, and nonholonomic spaces.
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. With a balance of survey papers and frontier research results, this book will appeal to graduate students and researchers alike.
Table of contents:
Part I.Quantum Groups, Representations of Groups and Algebras Ya. S. Solbelman and L. L. Vaksman: On some problems in the theory of quantum groups; E. Ye. Vaysleb: Representations of quantum *-algebras slt(N + 1, R) ; S. V. Kerov: Generalized Hall-Littlewood symmetric functions and orthogonal polynomials; A. M. Vershik and B. S. Tsirelson: Formulation of Bell type problems and "noncommutative" convex geometry; M. L. Nazarov: Projective representations of the infinite syummetric group; V. L. Ostrovskii and Yyu. S. Samollenko: Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation; L. I. Valnerman: Relations between compact quantum groups and Kac algebras; A. I. Barvinok: Combinatorial complexity of orbits in representations of the symmetric group; Part II. Dynamical Systems and Approximations A. M. Vershik and A. N. Livshits: Adic models of ergodic transformations, spectral theory, substitutions, and related topics; D. Yu. Burago: Periodic metrics; D. Yu. 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. N. Livshits: About a certain weakly mixing substitution; Vn N. Berestovskii and A. M. Vershik: Manifolds with intrinsic metric, and nonholonomic spaces.
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. With a balance of survey papers and frontier research results, this book will appeal to graduate students and researchers alike.