Characters of real special 2-groups

TL;DR

This paper presents methods to analyze real special 2-groups by leveraging quadratic maps to compute their conjugacy classes, complex representations, and characters, simplifying the understanding of their structure.

Contribution

It introduces novel techniques to determine conjugacy classes and characters of real special 2-groups solely through quadratic maps, advancing group representation theory.

Findings

Methods for computing conjugacy classes using quadratic maps

Procedures for deriving complex representations of real special 2-groups

Simplified approach to character calculation for these groups

Abstract

It is well-known that special 2-groups can be described in terms of quadratic maps over fields of characteristic 2. In this article we develop methods to compute conjugacy classes, complex representations and characters of a real special $2$-group using quadratic maps alone.