EKR Results for Cuspidal Representations of $\mathrm{GL}_2(q)$

Abstract

Let $\mathcal{S}_\chi$ be a cuspidal representation of $\mathrm{GL}_2(q)$. A subset $S \subseteq \mathrm{GL}_2(q)$ is \emph{$t$-intersecting} if $\dim_{\mathbb{C}}\{v \in \mathcal{S}_\chi: g_1v = g_2v\} \geqslant t$ for any $g_1, g_2 \in S$. In this paper, we determine $\max{|S|}$ where $S$ is $t$-intersecting.