A note on the classification of simple $SL_2(\bar{\mathbb{F}}_p)$-modules admitting $\bf T$-stable lines in cross characteristic

Junbin Dong

A note on the classification of simple $SL_2(\bar{\mathbb{F}}_p)$-modules admitting $\bf T$-stable lines in cross characteristic

Representation Theory 2026-03-17 v1

Authors: Junbin Dong

Abstract

Let $\bf T$ be the group of diagonal matrices in $SL_2(\bar{\mathbb{F}}_p)$ , where $p$ is a prime number. Let $\Bbbk$ be an algebraically closed field of characteristic not equal to $2$ and $p$ . We classify all the irreducible $\Bbbk$ -representations of $SL_2(\bar{\mathbb{F}}_p)$ that admit $\bf T$ -stable lines.

Keywords

SL2 modules T-stable lines representation theory finite fields irreducible representations

Cite

@article{arxiv.2603.13769,
  title  = {A note on the classification of simple $SL_2(\bar{\mathbb{F}}_p)$-modules admitting $\bf T$-stable lines in cross characteristic},
  author = {Junbin Dong},
  journal= {arXiv preprint arXiv:2603.13769},
  year   = {2026}
}

Comments

16 pages

Related papers

View all related →