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Journal of the London Mathematical Society 2002 66(3):592-604; doi:10.1112/S0024610702003472
© 2002 by London Mathematical Society
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© The London Mathematical Society

A Class of Rigid Coxeter Groups

Anton Kaul

Department of Mathematics, Tufts University Medford, MA 02155, USA, anton.kaul{at}tufts.edu

Received 8 March 2001. Revision received 20 December 2001.

A Coxeter group W is said to be rigid if, given any two Coxeter systems (W, S) and (W, S'), there is an automorphism {rho}: W -> W such that {rho}(S) = S'. The class of Coxeter systems (W, S) for which the Coxeter graph {Gamma}S is complete and has only odd edge labels is considered. (Such a system is said to be of type Kn.) It is shown that if W has a type Kn system, then any other system for W is also type Kn. Moreover, the multiset of edge labels on {Gamma}S and {Gamma}S' agree. In particular, if all but one of the edge labels of {Gamma}S are identical, then W is rigid.


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