Finite groups whose real irreducible representations have unique dimensions

TL;DR

This paper classifies finite groups based on the uniqueness of the dimensions of their real irreducible representations, providing a complete characterization of such groups.

Contribution

It offers a complete classification of finite groups with real irreducible representations of distinct degrees, a novel result in representation theory.

Findings

Identifies all finite groups with unique real irreducible representation dimensions

Provides explicit criteria for the classification

Advances understanding of the structure of finite groups in relation to their representations

Abstract

We determine the finite groups whose real irreducible representations have different degrees.