A supercharacter theory for $PSL(2,q)$ and $SO(3,q)$

Source abstract

The concept of a supercharacter theory for a finite group was introduced in 2008 by Diaconis and Isaacs in [6]. In their article the notion of irreducible characters and conjugacy classes is generalized to supercharacters and superclasses while still maintaining important information about the group. This article continues an investigation of a specific supercharacter theory where the supercharacters are taken to be sums of irreducible characters of the same degree. We show this supercharacter theory construction can be done for all projective special linear groups $PSL(2,q)$ and all special orthogonal groups $SO(3,q)$ where $q$ is any power of an even or odd prime.Accepted: 12 April 2025