The geometry of the chamber system of a semimodular lattice

DOI10.1007/BF00383400zbMath0738.06010OpenAlexW2068577099MaRDI QIDQ1182062

Herbert Abels

Publication date: 27 June 1992

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00383400

zbMATH Keywords

metric spacesymmetric groupsemimodular latticebuildingschamber systemmaximal chainsgallery distanceJordan-Hölder permutationSchubert symbolWeyl-group valued distance functions

Mathematics Subject Classification ID

Geometric group theory (20F65) Semimodular lattices, geometric lattices (06C10)

Related Items (12)

Diagrams and rectangular extensions of planar semimodular lattices ⋮ Quasiplanar diagrams and slim semimodular lattices ⋮ Minimal paths between maximal chains in finite rank semimodular lattices ⋮ Semimodular lattices and semibuildings ⋮ Note on the description of join-distributive lattices by permutations ⋮ The gallery distance of flags ⋮ A nonpositive curvature property of modular semilattices ⋮ Coordinatization of finite join-distributive lattices. ⋮ Finite convex geometries of circles ⋮ Representations of matroids in semimodular lattices ⋮ Combinatorial flag varieties ⋮ Characterizing flag graphs and incuced subgraphs of Cartesian product graphs

Cites Work

• Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
• Gated sets in metric spaces
• The gallery distance of flags
• Buildings of spherical type and finite BN-pairs
• Supersolvable lattices
• Shellable and Cohen-Macaulay Partially Ordered Sets
• Unnamed Item

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