On the ranks of string C-group representations for symplectic and orthogonal groups

DOI10.1090/conm/764/15329OpenAlexW3147564676MaRDI QIDQ4998738

Peter A. Brooksbank

Publication date: 9 July 2021

Published in: Polytopes and Discrete Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.05512

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Polyhedra and polytopes; regular figures, division of spaces (51M20) Group actions on manifolds and cell complexes in low dimensions (57M60) Simple groups: alternating groups and groups of Lie type (20D06) Helly-type theorems and geometric transversal theory (52A35) Symmetry properties of polytopes (52B15) Representation theory of groups (20Cxx)

Uses Software

• Magma

Cites Work

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• Three-dimensional classical groups acting on polytopes
• Polytopes of high rank for the symmetric groups
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• A new Petrie-like construction for abstract polytopes
• Generating triples of involutions of alternating groups
• The Magma algebra system. I: The user language
• Orthogonal groups in characteristic 2 acting on polytopes of high rank
• Generating triples of involutions of Chevalley groups over a finite field of characteristic 2
• Generators for Alternating and Symmetric Groups
• MORE ON GENERATORS FOR ALTERNATING AND SYMMETRIC GROUPS
• Abstract Regular Polytopes
• String C-group representations of alternating groups
• Rank reduction of string C-group representations
• Groups of type L ₂(q) acting on polytopes
• Polytopes of large rank for \(\mathrm{PSL}(4,\mathbb{F}_q)\)

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