A general tensor product theorem

TL;DR

This paper proves that any admissible irreducible representation of a product of two locally compact groups can be decomposed into a tensor product of irreducible representations of each individual group, generalizing existing theories.

Contribution

It establishes a general tensor product theorem for admissible irreducible representations of product groups, extending the understanding of their structure.

Findings

Every admissible irreducible representation of a product group is a tensor product of irreducible representations of the factors.

The result applies to locally compact groups, broadening previous specific cases.

Provides a foundational tool for analyzing representations in harmonic analysis and related fields.

Abstract

We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.