Real irreducible representations of SL(2,q) and their fixed point dimensions for cyclic subgroups

TL;DR

This paper computes the characters of real irreducible representations of SL(2,q) for odd prime q and determines their fixed point dimensions under cyclic subgroup actions, enhancing understanding of the group's representation structure.

Contribution

It provides explicit character formulas and fixed point dimensions for real irreducible representations of SL(2,q), a novel detailed analysis for this class of groups.

Findings

Character formulas for real irreducible representations of SL(2,q)

Dimensions of fixed points under cyclic subgroup actions

Enhanced understanding of representation structure of SL(2,q)

Abstract

We compute the characters of real irreducible representations of SL(2,q), the special linear group on q letters, for an odd prime $q$. Moreover, we give the dimensions of these irreducible representations under the actions of cyclic subgroups of SL(2,q).