Non-crossing partition lattices in finite real reflection groups
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Publication:5437623
DOI10.1090/S0002-9947-07-04282-1zbMath1187.20051arXivmath/0501502MaRDI QIDQ5437623
Publication date: 21 January 2008
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0501502
simplicial complexespartially ordered setsCoxeter elementsproducts of reflectionsreflection lengthsfinite irreducible real reflection groups
Partitions of sets (05A18) Combinatorics of partially ordered sets (06A07) Reflection and Coxeter groups (group-theoretic aspects) (20F55)
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Cites Work
- Unnamed Item
- A new approach to the word and conjugacy problems in the braid groups
- Non-positively curved aspects of Artin groups of finite type
- Non-crossing partitions for classical reflection groups
- \(Y\)-systems and generalized associahedra
- Bestvina's normal form complex and the homology of Garside groups.
- \(K(\pi,1)\)'s for Artin groups of finite type.
- Springer theory in braid groups and the Birman-Ko-Lee monoid.
- Sur les partitions non croisées d'un cycle. (The non-crossed partitions of a cycle)
- The dual braid monoid
- Finite Reflection Groups
- Groupes et algébras de Lie
- Noncrossing Partitions for the GroupDn
- A PARTIAL ORDER ON THE ORTHOGONAL GROUP
- THE BRAID GROUP AND OTHER GROUPS
- Reflection groups and invariant theory
- A partial order on the symmetric group and new \(K(\pi,1)\)'s for the braid groups
- Artin groups of finite type with three generators