Alternating subgroups of Coxeter groups
نویسندگان
چکیده
We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.
منابع مشابه
On the Isomorphism Problem for Finitely Generated Coxeter Groups. I Basic Matching
The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [3] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper, we determine some stro...
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Coxeter groups are familiar objects in many branches of mathematics. The connections with semisimple Lie theory have been a major motivation for the study of Coxeter groups. (Crystallographic) Coxeter groups are involved in Kac-Moody Lie algebras, which generalize the entire theory of semisimple Lie algebras. Coxeter groups of nite order are known to be nite re ection groups, which appear in in...
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For W a finite Coxeter group, a formula is found for the size of W equivalence classes of subsets of a base. The proof is a case-by-case analysis using results and tables of Orlik and Solomon. As a corollary we obtain an alternating sum identity which generalizes a well-known identity from the theory of Coxeter groups.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 115 شماره
صفحات -
تاریخ انتشار 2008