On Mackey Decomposition for locally profinite groups

TL;DR

This paper explores generalizations of Mackey's decomposition theory for locally profinite groups, establishing conditions for its validity and providing examples where it fails, thereby extending the understanding of induced representations.

Contribution

It introduces new conditions for Mackey decomposition applicability in locally profinite groups and presents examples illustrating its limitations.

Findings

Identified conditions under which Mackey decomposition holds for locally profinite groups

Provided examples demonstrating failure of Mackey decomposition in certain cases

Extended Mackey's theory to a broader class of groups

Abstract

To study induced representation of some class of groups, Mackey's theory is very useful. In this paper, we consider some generalization of Mackey's theory for locally profinite groups. In particular, we give conditions on groups under which we have the Mackey decomposition and some examples such that we do not have the Mackey decomposition in some sense.