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.
Screenings and a universal Lie-de Rham cocycle by V. Ginzburg and V. Schechtman Interlacing measures by S. Kerov Quasicommuting families of quantum Plucker coordinates by B. Leclerc and A. Zelevinsky Factorial supersymmetric Schur functions and super Capelli identities by A. Molev Yangians and Capelli identities by M. L. Nazarov Hinges and the Study-Semple-Satake-Furstenberg-De Concini-Procesi-Oshima boundary by Y. Neretin Multiplicities and Newton polytopes by A. Okounkov Shifted Schur functions II. The binomial formula for characters of classical groups and its applications by A. Okounkov and G. Olshanski.