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On quotients of Coxeter groups under the weak order

✍ Scribed by Debra J. Waugh


Book ID
108421665
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
133 KB
Volume
30
Category
Article
ISSN
0196-8858

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✍ Tetsuya Hosaka πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 115 KB

In this paper, using a result of F.T. Farrell, we reformulate the Davis formula for the cohomology of a Coxeter group, and we study the problem as to when the ith cohomology of a Coxeter group is ΓΏnitely generated.

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Let W, S be any finite Coxeter system and F the Bruhat᎐Chevalley Ε½ . Ε½ . order on W. We denote by Base W and BiGr W the base and the set of all bi-grassmannians, respectively. For s, t g S we let s W t be the subset of Ε½ . Ε½ . Γ„ 4 Ε½ . Γ„ 4 BiGr W consisting of all w g W such that L L w s s and R R w