On the regularity of the finite reflection groups
R. B. Howlett and Jian-yi Shi
Research Report 98-7
Date: 17 March 1998
We show that an irreducible finite reflection group G of rank greater than 1
is regular if and only if the associated root system is perfect. This holds
if and only if G is a Coxeter group. Hence we get a characterization of
Coxeter groups among all the irreducible finite reflection groups of rank
greater than 1.
finite reflection groups. Coxeter groups. root systems.
AMS Subject Classification (1991)
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Sydney Mathematics and Statistics