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arXiv · 2604.01953

An Erdős-Ko-Rado result for some principal series representations

Jiaqi Liao·Guiying Yan
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Abstract

Let $V$ be an irreducible principal series representation of $\mathrm{GL}_2(q)$ satisfying certain conditions. Two subsets $S_1, S_2 \subseteq \mathrm{GL}_2(q)$ are called cross-$t$-intersecting if $\dim\{v \in V: g_1v = g_2v\} \geqslant t$ for any $(g_1, g_2) \in S_1 \times S_2$. In this paper, we determine $\max(|S_1|\cdot|S_2|)$ where $S_1, S_2 \subseteq \mathrm{GL}_2(q)$ are cross-$1$-intersecting. Our proofs are based on eigenvalue techniques and the representation theory of $\mathrm{GL}_2(q)$.

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Jiaqi Liao, Guiying Yan. 2026-04-13. An Erdős-Ko-Rado result for some principal series representations. https://arxiv.org/abs/2604.01953

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