Trivial source character tables of $\text{SL}_2(q)$, Part II

TL;DR

This paper computes the trivial source character tables of the groups SL_2(q) for even q over a suitable field, extending previous work that focused on odd q in cross-characteristic.

Contribution

It provides the explicit computation of trivial source character tables for SL_2(q) with even q, filling a gap in the existing literature.

Findings

Computed trivial source character tables for SL_2(q) with even q

Extended previous results from odd q to even q cases

Contributed to the understanding of trivial source rings in finite groups

Abstract

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups $\text{SL}_{2}(q)$ for $q$ even, over a large enough field $k$ of positive characteristic ${\ell}$ not dividing $q$. This article is a continuation of our article Trivial Source Character Tables of $\text{SL}_{2}(q)$ where we considered, in particular, the case in which $q$ is odd in cross-characteristic.