eBook ISBN:  9781470433925 
Product Code:  TRANS2/181.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470433925 
Product Code:  TRANS2/181.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 181; 1998; 271 ppMSC: Primary 05; 17; 22; Secondary 53
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.
ReadershipGraduate students, research mathematicians, and mathematical physicists interested in representation theory, infinite dimensional Lie algebras, quantum groups, and algebraic combinatorics.

Table of Contents

Chapters

Victor Ginzburg and Vadim Schechtman — Screenings and a universal Liede 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 StudySempleSatakeFurstenbergDe ConciniProcesiOshima 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


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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.

Chapters

Victor Ginzburg and Vadim Schechtman — Screenings and a universal Liede 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 StudySempleSatakeFurstenbergDe ConciniProcesiOshima 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