Quotients of Coxeter complexes and buildings with linear diagram (Q1821349)
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scientific article; zbMATH DE number 3998630
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quotients of Coxeter complexes and buildings with linear diagram |
scientific article; zbMATH DE number 3998630 |
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Quotients of Coxeter complexes and buildings with linear diagram (English)
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1986
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The author investigates certain subcomplexes of Coxeter complexes and (Tits) buildings, called quotient Coxeter complexes and quotient buildings. It is shown that such a quotient is the order complex of a poset if and only if it has a linear Coxeter diagram. Moreover it is shown that the poset (with a top and bottom element adjoined) is a lattice (for Coxeter complexes and for non-quotient buildings) and is lexicographically shellable (for both quotient Coxeter complexes and quotient buildings).
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Coxeter group
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shellability
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quotient Coxeter complexes
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quotient buildings
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