Description of the Characters and Factor Representations of Infinite Symmetric Inverse Semigroup

TL;DR

This paper classifies all indecomposable characters of the infinite symmetric semigroup, revealing only one new parameter compared to the infinite symmetric group, based on representation theory insights.

Contribution

It provides a complete list of indecomposable characters for the infinite symmetric semigroup, extending known results from the infinite symmetric group with minimal new parameters.

Findings

Complete classification of indecomposable characters

Introduction of one new parameter with combinatorial meaning

Connection to representation theory of finite and infinite symmetric groups

Abstract

We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial meaning. The paper relies on the representation theory of the finite symmetric semigroups and the representation theory of the infinite symmetric group.