Representations of the Infinite Symmetric Group

Introduction
Part I. Symmetric Functions and Thoma's Theorem:
1. Preliminary facts from representation theory of finite symmetric groups
2. Theory of symmetric functions
3. Coherent systems on the Young graph
4. Extreme characters and Thoma's Theorem
5. A toy model (the Pascal Graph) and de Finetti's Theorem
6. Asymptotics of relative dimension in the Young graph
7. Boundaries and Gibbs measures on paths
Part II. Unitary Representations:
8. Preliminaries and Gelfand pairs
9. Classification of general spherical type representations
10. Realization of irreducible spherical representations of (S(∞) × S(∞), diagS(∞))
11. Generalized regular representations Tz
12. Disjointness of representations Tz
References
Index.