Reflection groups and polytopes over finite fields, II
| dc.creator | Monson, Barry | |
| dc.creator | Schulte, Egon | |
| dc.date | 2006-01-20 | |
| dc.date.accessioned | 2026-07-07T06:59:08Z | |
| dc.date.available | 2026-07-07T06:59:08Z | |
| dc.description | When the standard representation of a crystallographic Coxeter group $Γ$ is reduced modulo an odd prime $p$, a finite representation in some orthogonal space over $\mathbb{Z}_p$ is obtained. If $Γ$ has a string diagram, the latter group will often be the automorphism group of a finite regular polytope. In Part I we described the basics of this construction and enumerated the polytopes associated with the groups of rank 3 and the groups of spherical or Euclidean type. In this paper, we investigate such families of polytopes for more general choices of $Γ$, including all groups of rank 4. In particular, we study in depth the interplay between their geometric properties and the algebraic structure of the corresponding finite orthogonal group. | |
| dc.description | 30 pages (Advances in Applied Mathematics, to appear) | |
| dc.identifier | https://arxiv.org/abs/math/0601502 | |
| dc.identifier | http://arxiv.org/abs/math/0601502 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107636 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 51M20; 20F55 | |
| dc.title | Reflection groups and polytopes over finite fields, II | |
| dc.type | text |