Characters and invariant random subgroups of the finitary symmetric group

2018/12/06 by Thomas, Simon
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1812.02694

Abstract

We will describe the relationship between the indecomposable characters of the finitary symmetric group and its ergodic invariant random subgroups; and we will interpret each Thoma character as an asymptotic limit of a naturally associated sequence of characters induced from linear characters of Young subgroups of finite symmetric groups.

Related

• Character Theory of Symmetric Groups, Subgroup Growth of Fuchsian Groups, and Random Walks
• A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra
• The central limit theorem for extremal characters of the infinite symmetric group
• Invariant random subgroups of strictly diagonal limits of finite symmetric groups
• Martingales and character ratios