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A Class of Rigid Coxeter Groups
Author(s) -
Kaul Anton
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003472
Subject(s) - coxeter group , combinatorics , mathematics , longest element of a coxeter group , point group , multiset , coxeter complex , coxeter graph , class (philosophy) , coxeter element , artin group , graph , type (biology) , pure mathematics , computer science , voltage graph , line graph , artificial intelligence , ecology , biology
A Coxeter group W is said to be rigid if, given any two Coxeter systems ( W , S ) and ( W , S ′), there is an automorphism ρ: W → W such that ρ( S ) = S ′. The class of Coxeter systems ( W , S ) for which the Coxeter graph Γ S is complete and has only odd edge labels is considered. (Such a system is said to be of type K n .) It is shown that if W has a type K n system, then any other system for W is also type K n . Moreover, the multiset of edge labels on Γ S and Γ S ′ agree. In particular, if all but one of the edge labels of Γ S are identical, then W is rigid.