The set of dominance-minimal roots

DOI10.1006/jabr.1997.7418zbMath0942.20020OpenAlexW2014803182MaRDI QIDQ1270077

Brigitte Brink

Publication date: 21 February 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1997.7418

zbMATH Keywords

Coxeter groupsCoxeter systemsroot systemselementary rootsdominance minimal roots

Mathematics Subject Classification ID

Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Related Items (13)

Automata, reduced words and Garside shadows in Coxeter groups. ⋮ Preprojective roots and graph monoids of Coxeter groups ⋮ Small roots, low elements, and the weak order in Coxeter groups ⋮ NONORTHOGONAL GEOMETRIC REALIZATIONS OF COXETER GROUPS ⋮ The dominance hierarchy in root systems of Coxeter groups. ⋮ Polytopal realizations of finite type \(\mathbf{g}\)-vector fans ⋮ Automorphisms of Coxeter groups of rank three ⋮ Coxeter systems for which the Brink-Howlett automaton is minimal ⋮ Semidirect Product Decomposition of Coxeter Groups ⋮ Universal Reflection Subgroups and Exponential Growth in Coxeter Groups ⋮ Computation in Coxeter groups II. Constructing minimal roots ⋮ Elementary roots and admissible subsets of Coxeter groups ⋮ Garside families in Artin-Tits monoids and low elements in Coxeter groups.

Cites Work

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• The reflection representations of some Chevalley groups
• A finiteness property and an automatic structure for Coxeter groups
• Machine calculations in Weyl groups

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