On the Weak Order of Coxeter Groups

DOI10.4153/CJM-2017-059-0MaRDI QIDQ4632763

Matthew J. Dyer

Publication date: 30 April 2019

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.5557

zbMATH Keywords

latticeCoxeter grouproot systemweak order

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Complete lattices, completions (06B23) Root systems (17B22)

Related Items (20)

On inversion sets and the weak order in Coxeter groups ⋮ Affine twisted length function ⋮ Imaginary cones and limit roots of infinite Coxeter groups ⋮ Lattice homomorphisms between weak orders ⋮ Biclosed sets in affine root systems ⋮ Local finiteness of the twisted Bruhat orders on affine Weyl groups ⋮ Lattice structure of grid-Tamari orders ⋮ On conjugacy of abstract root bases of root systems of Coxeter groups ⋮ Tamari lattices for parabolic quotients of the symmetric group ⋮ Twisted weak orders of Coxeter groups ⋮ The maximum cardinality of minimal inversion complete sets in finite reflection groups ⋮ Oriented matroid structures from realized root systems ⋮ Imaginary cone and reflection subgroups of Coxeter groups ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The CDE property for skew vexillary permutations ⋮ Infinite reduced words, lattice property and braid graph of affine Weyl groups ⋮ Reduced expression of minimal infinite reduced words of affine Weyl groups ⋮ Cone types, automata, and regular partitions in Coxeter groups ⋮ Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras

Cites Work

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• Geometric combinatorics of Weyl groupoids.
• Hyperplane arrangements with a lattice of regions
• Reflection subgroups of Coxeter systems
• Weyl groupoids with at most three objects.
• Large convex sets in oriented matroids
• Meet-distributive lattices and the anti-exchange closure
• Decompositions of root systems
• Normalizers of parabolic subgroups in Coxeter groups
• Quotients of twisted Bruhat orders
• Bruhat intervals, polyhedral cones and Kazhdan-Lusztig-Stanley polynomials
• Sets of reflections defining twisted Bruhat orders.
• A generalization of Coxeter groups, root systems, and Matsumoto's theorem.
• Combinatorics of Coxeter Groups
• Semidirect Product Decomposition of Coxeter Groups
• On Closed Subsets of Root Systems
• Oriented Matroids
• On Centralizers of Reflections in Coxeter Groups
• Convex Geometries on Root Systems

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