Frobenius Reciprocity for Topological Groups

TL;DR

This paper explores the conditions under which restriction functors in various categories of topological group representations have adjoints, enhancing understanding of representation theory in topological settings.

Contribution

It establishes the existence of left and right adjoints to restriction functors across discrete, linear complete, and compact topological groups.

Findings

Identifies conditions for adjoint functors in different topological group categories.

Provides new insights into the structure of continuous representations.

Extends Frobenius reciprocity to broader topological contexts.

Abstract

We investigate the existence of left and right adjoints to the restriction functor in three categories of continuous representations of a topological group: discrete, linear complete and compact.