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RIGIDITY OF COXETER GROUPS AND ARTIN GROUPS NOEL BRADY1, JONATHAN P. MCCAMMOND2, BERNHARD MUHLHERR,
 

Summary: RIGIDITY OF COXETER GROUPS AND ARTIN GROUPS
NOEL BRADY1, JONATHAN P. MCCAMMOND2, BERNHARD M¨UHLHERR,
AND WALTER D. NEUMANN3
Abstract. A Coxeter group is rigid if it cannot be defined by two
nonisomorphic diagrams. There have been a number of recent results
showing that various classes of Coxeter groups are rigid, and a particu-
larly interesting example of a nonrigid Coxeter group has been given in
[17]. We show that this example belongs to a general operation of "di-
agram twisting". We show that the Coxeter groups defined by twisted
diagrams are isomorphic, and, moreover, that the Artin groups they de-
fine are also isomorphic, thus answering a question posed by Charney.
Finally, we show a number of Coxeter groups are reflection rigid once
twisting is taken into account.
Contents
1. Basic definitions 2
2. Prior results on rigidity 4
3. Reflection rigidity 6
4. Diagram twisting 9
5. Rigidity of trees 13
6. Additional examples 16

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics