Representations of 2-transitive topological groups

TL;DR

This paper extends Burnside's Lemma to 2-transitive topological groups, showing that compact groups have finite, reducible representations, while noncompact groups have irreducible representations, revealing structural differences.

Contribution

It introduces an analogue of Burnside's Lemma for 2-transitive topological groups, detailing the nature of their representations based on compactness.

Findings

Compact groups have finite, reducible representations including constant functions.

Noncompact groups have irreducible representations.

Representation structure depends on the group's compactness.

Abstract

An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group and representation space are noncompact the representation is irreducible