Trivial source character tables of SL(2,q)

TL;DR

This paper computes the trivial source character tables of SL(2,q) groups over large fields of positive characteristic using character-theoretical methods, covering various cases based on q and the characteristic.

Contribution

It provides explicit computations of trivial source character tables for SL(2,q) groups in specific cases, expanding understanding of their modular representation theory.

Findings

Computed trivial source character tables for SL(2,q) when q is odd.

Derived tables for cases where ivides (q) or q3 mod 8.

Applied character-theoretical methods to obtain these tables.

Abstract

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL(2,q) over a large enough field of positive characteristic $\ell$ via character-theoretical methods in the cases in which $q$ is odd, $\ell \mid (q\pm1)$ when~$\ell$ is odd, and $q\equiv \pm 3\pmod{8}$ when $\ell=2$.