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High-Dimensional Expanders from Chevalley Groups O'Donnell, Ryan Pratt, Kevin High-dimensional expanders simplicial complexes group theory Let Φ be an irreducible root system (other than G₂) of rank at least 2, let 𝔽 be a finite field with p = char 𝔽 > 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 = A_d. Our work gives three new families of spectral HDXs of any dimension ≥ 2, and four exceptional constructions of dimension 4, 6, 7, and 8. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ryan O'Donnell and Kevin Pratt 2022 Is Part Of LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2022.18 urn:nbn:de:0030-drops-165802 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.18 eng https://creativecommons.org/licenses/by/4.0/legalcode