Kirillov’s Seminar on Representation Theory
About this Title
G. I. Olshanski, Institute for Problems of Information Transmission, Moscow, Russia, Editor
Publication: American Mathematical Society Translations: Series 2
Publication Year 1998: Volume 181
ISBNs: 978-0-8218-0669-2 (print); 978-1-4704-3392-5 (online)
MathSciNet review: MR1618767
MSC: Primary 17-06; Secondary 00B25, 05-06
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 paper—the 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 measures—describes 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.
Graduate students, research mathematicians, and mathematical physicists interested in representation theory, infinite dimensional Lie algebras, quantum groups, and algebraic combinatorics.
Table of Contents
- Victor Ginzburg and Vadim Schechtman – Screenings and a universal Lie-de Rham cocycle
- Sergei Kerov – Interlacing measures
- Bernard Leclerc and Andrei Zelevinsky – Quasicommuting families of quantum Plücker coordinates
- Alexander Molev – Factorial supersymmetric Schur functions and super Capelli identities
- Maxim Nazarov – Yangians and Capelli identities
- Yurii A. Neretin – Hinges and the Study-Semple-Satake-Furstenberg-De Concini-Procesi-Oshima boundary
- Andreĭ Okounkov – Multiplicities and Newton polytopes
- Andreĭ Okounkov and Grigori Olshanski – Shifted Schur functions II. The binomial formula for characters of classical groups and its applications