Complex Representations of Groups and Involutions of its Automorphisms
Representation Theory
2026-05-25 v1 Combinatorics
Group Theory
Abstract
In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these quantities in the context of inner automorphisms and the symmetric group . As an application, we provide a criterion for identifying groups that possess complex (non-real) irreducible representations and explore the structural consequences arising from these results.
Cite
@article{arxiv.2605.23195,
title = {Complex Representations of Groups and Involutions of its Automorphisms},
author = {Venkata Subbaiah Yerrapati and Rahul Dixit and Ajay Kumar Shukla},
journal= {arXiv preprint arXiv:2605.23195},
year = {2026}
}