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[2203.03705] High-Dimensional Expanders from Chevalley Groups
source link: https://arxiv.org/abs/2203.03705
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[Submitted on 7 Mar 2022]
High-Dimensional Expanders from Chevalley Groups
Let Φ be an irreducible root system (other than G2) of rank at least 2, let F be a finite field with p=charF>3, and let G(Φ,F) be the corresponding Chevalley group. We describe a strongly explicit high-dimensional expander (HDX) family of dimension rank(Φ), where G(Φ,F) acts simply transitively on the top-dimensional faces; these are λ-spectral HDXs with λ→0 as p→∞. This generalizes a construction of Kaufman and Oppenheim (STOC 2018), which corresponds to the case Φ=Ad. Our work gives three new families of spectral HDXs of any dimension ≥2, and four exceptional constructions of dimension 4, 6, 7, and 8.
| Subjects: | Discrete Mathematics (cs.DM); Group Theory (math.GR) |
| Cite as: | arXiv:2203.03705 [cs.DM] |
| (or arXiv:2203.03705v1 [cs.DM] for this version) | |
| https://doi.org/10.48550/arXiv.2203.03705 |
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