Indecomposable characters on direct limit of symmetric groups with diagonal embeddings

TL;DR

This paper classifies all indecomposable characters of inductive limits of symmetric groups with diagonal embeddings, providing a complete description and full classification of these groups.

Contribution

It offers the first complete description of indecomposable characters for these inductive limits and classifies their isomorphism classes.

Findings

Complete characterization of indecomposable characters

Full classification of inductive limit groups

Insights into the structure of symmetric group limits

Abstract

In this paper we obtain the complete description of all indecomposable characters (central positive-definite functions) of inductive limits of the symmetric groups under block diagonal embedding. As a corollary we obtain the full classification of the isomorphism classes of these inductive limits.