Parabolic Subgroups of Artin Groups of Type Fc

نویسندگان

  • Eddy Godelle
  • EDDY GODELLE
چکیده

The group AS is called an Artin group and relations sts . . . } {{ } ms,t terms = tst . . . } {{ } ms,t terms are called braid relations. For instance, if S = {s1, . . . , sn} with msi,sj = 3 for |i − j| = 1 and msi,sj = 2 otherwise, then the associated Artin group is the braid group. We denote by A+S the submonoid of AS generated by S. This monoid A+S has the same presentation as the group AS , considered as a monoid presentation ([11]). When we add relations s2 = 1 to the presentation of AS we obtain the Coxeter group WS associated to AS . We say that AS is spherical if WS is finite. The matrix M may be represented by a graph denoted by ΓS , whose set of vertices is S and where an edge joins two vertices if ms,t ≥ 3; these edges are labelled by ms,t if ms,t ≥ 4. We say that AS (or simply S) is indecomposable if the graph ΓS is connected. A subgroup AT of AS generated by a part T of S is called a standard parabolic subgroup, and a subgroup of AS conjugate to a standard parabolic subgroup is called a parabolic subgroup. Van Der Lek showed ([14]) that (AT , T ) is canonically isomorphic to the Artin-Tits system associated to the matrix (ms,t)s,t∈T ; its graph ΓT is the full subgraph of ΓS generated by T . The

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تاریخ انتشار 2003