American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1998; 271 pp; hardcover Volume: 181 ISBN10: 0821806696 ISBN13: 9780821806692 List Price: US$120 Member Price: US$96 Order Code: TRANS2/181
 This book is a collection of selected papers written by students and active participants of the A. A. Kirillov seminar on representation theory held at Moscow University. The papers deal with various aspects of representation theory for Lie algebras and Lie groups, and its relationship to algebraic combinatorics, the theory of quantum groups and geometry. This volume reflects current research interests of the leading representatives of the Russian school of representation theory. Readers will find both a variety of new results (for such quickly developing fields as infinite dimensional algebras and quantum groups) and a new look at classical aspects of the theory. Among the contributions, S. Kerov's paperthe first survey of various topics in representation theory of the infinite symmetric groups, classical orthogonal polynomials, Markov's moment problem, random measures, and operator theory, unified around the concept of interlacing measuresdescribes the unexpected relationships between distant domains of mathematics, and an expository paper by Y. Neretin presents a new geometric approach to boundaries and compactifications of reductive groups and symmetric spaces. Readership Graduate students, research mathematicians, and mathematical physicists interested in representation theory, infinite dimensional Lie algebras, quantum groups, and algebraic combinatorics. Table of Contents  V. Ginzburg and V. Schechtman  Screenings and a universal Liede Rham cocycle
 S. Kerov  Interlacing measures
 B. Leclerc and A. Zelevinsky  Quasicommuting families of quantum Plücker coordinates
 A. Molev  Factorial supersymmetric Schur functions and super Capelli identities
 M. L. Nazarov  Yangians and Capelli identities
 Y. Neretin  Hinges and the StudySempleSatakeFurstenbergDe ConciniProcesiOshima boundary
 A. Okounkov  Multiplicities and Newton polytopes
 A. Okounkov and G. Olshanski  Shifted Schur functions II. The binomial formula for characters of classical groups and its applications
