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PreprintCC BY 4.0arXiv

EKR Results for Cuspidal Representations of GL2(q)

  • Jiaqi Liao
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Abstract

Let ๐’ฎฯ‡ be a cuspidal representation of GL2(q). A subset S โŠ† GL2(q) is t-intersecting if dimโ„‚{v โˆˆ ๐’ฎฯ‡: g1v = g2v} geqslant t for any g1, g2 โˆˆ S. For q = pf, where p is an odd prime, f geqslant 2, and 1 leqslant t < p is an integer, we determine the maximum size of an t-intersecting subset when ฯ‡(โˆ’1) = โˆ’1, and when ฯ‡(โˆ’1) = 1 with t leqslant 2. The proof combines explicit fixed-space dimensions, attaining subgroup constructions, and weighted spectral bounds for normal Cayley graphs.

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Cite

BibTeXRIS
BibTeX
@misc{liao2026results,
  title = {{EKR Results for Cuspidal Representations of $\mathrmGL_2(q)$}},
  author = {Jiaqi Liao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38472},
  eprint = {2610.38472},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38472},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - EKR Results for Cuspidal Representations of GL_2(q)
AU  - Jiaqi Liao
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38472
UR  - https://arxiv.org/abs/2610.38472
AB  - Let ๐’ฎ_ฯ‡ be a cuspidal representation of GL_2(q). A subset S โŠ† GL_2(q) is t-intersecting if dim_โ„‚{v โˆˆ ๐’ฎ_ฯ‡: g_1v = g_2v} geqslant t for any g_1, g_2 โˆˆ S. For q = p^f, where p is an odd prime, f geqslant 2, and 1 leqslant t < p is an integer, we determine the maximum size of an t-intersecting subset when ฯ‡(โˆ’1) = โˆ’1, and when ฯ‡(โˆ’1) = 1 with t leqslant 2. The proof combines explicit fixed-space dimensions, attaining subgroup constructions, and weighted spectral bounds for normal Cayley graphs.
ER  -