Semigroup approach to admissible representations of the infinite symmetric group

I. E. Devyatkova<sup>ab

a</sup> HSE University, Moscow, Russia
^b Igor Krichever Centeк for Advanced Studies, Skolkovo Institute of Science and Technology, Moscow, Russia

Abstract: Let $S(\infty)$ denote the group of finitary permutations of the set $\mathbb N:=\{1,2,3,\dots\}$. It is a countable group admitting a lot of different topologies compatible with the group structure. In particular, such topologies arise from partitions of the set $\mathbb N$ into blocks of infinite size. The corresponding categories of continuous unitary representations of $S(\infty)$ were studied by Nessonov (Sbornik: Mathematics, 2012). We propose a different approach to his classification results based on the so-called semigroup method. Some additional information is also obtained.

Key words and phrases: Infinite symmetric group, Young subgroups, admissible representations, semigroups.

UDC: 517.981,517.986.7

Received: 18.09.2025

Language: English