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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.01953 |
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| _version_ | 1866913025762525184 |
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| author | Liao, Jiaqi Yan, Guiying |
| author_facet | Liao, Jiaqi Yan, Guiying |
| contents | 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 $\mathrm{GL}_2(q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01953 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Erdős-Ko-Rado result for some principal series representations Liao, Jiaqi Yan, Guiying Combinatorics 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 $\mathrm{GL}_2(q)$. |
| title | An Erdős-Ko-Rado result for some principal series representations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.01953 |