Convex Geometries on Root Systems

DOI10.1080/00927870600778340zbMath1103.52001OpenAlexW2062351463MaRDI QIDQ5491359

Annette Pilkington

Publication date: 11 October 2006

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

Full work available at URL: https://doi.org/10.1080/00927870600778340

zbMATH Keywords

Coxeter groupsmatroidsroot systemsclosure operatorsconvex geometries

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Simple, semisimple, reductive (super)algebras (17B20) Galois correspondences, closure operators (in relation to ordered sets) (06A15)

Related Items

On inversion sets and the weak order in Coxeter groups ⋮ A combinatorial rule for (co)minuscule Schubert calculus ⋮ Fully commutative elements and spherical nilpotent orbits ⋮ Root polytopes and abelian ideals ⋮ On the Weak Order of Coxeter Groups ⋮ The Weak Order on Weyl Posets ⋮ On conjugacy of abstract root bases of root systems of Coxeter groups ⋮ Twisted weak orders of Coxeter groups ⋮ Unnamed Item ⋮ Sortable elements in infinite Coxeter groups ⋮ Noncrossing partitions and representations of quivers

Cites Work

• The theory of convex geometries
• A finiteness property and an automatic structure for Coxeter groups
• Normalizers of Parabolic Subgroups of Reflection Groups
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