Representations of the Infinite Symmetric Group

Content: Cover
 Half-title page
 Series page
 Title page
 Copyright page
 Contents
 Introduction
 Part One Symmetric functions and Thoma's theorem
 1 Preliminary Facts From Representation Theory of Finite Symmetric Groups
 1.1 Exercises
 1.2 Notes
 2 Theory of Symmetric Functions
 2.1 Exercises
 2.2 Notes
 3 Coherent Systems on the Young Graph
 3.1 The Infinite Symmetric Group and the Young Graph
 3.2 Coherent Systems
 3.3 The Thoma Simplex
 3.4 Integral Representation of Coherent Systems and Characters
 3.5 Exercises
 3.6 Notes
 4 Extreme Characters and Thoma's Theorem
 4.1 Thoma's Theorem. 7.4 Gibbs Measures7.5 Examples of Path Spaces for Branching Graphs
 7.6 The Martin Boundary and the Vershik-Kerov Ergodic Theorem
 7.7 Exercises
 7.8 Notes
 Part Two Unitary representations
 8 Preliminaries and Gelfand Pairs
 8.1 Exercises
 8.2 Notes
 9 Classification of General Spherical Type Representations
 9.1 Notes
 10 Realization of Irreducible Spherical Representations of (S(∞) × S(∞), diagS(∞))
 10.1 Exercises
 10.2 Notes
 11 Generalized Regular Representations T[sub(z)]
 11.1 Exercises
 11.2 Notes
 12 Disjointness of Representations T[sub(z)]
 12.1 Preliminaries 12.2 Reduction to Gibbs Measures12.3 Exclusion of Degenerate Paths
 12.4 Proof of Disjointness
 12.5 Exercises
 12.6 Notes
 References
 Index.