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.

Key phrases

finite reflection groups. Coxeter groups. root systems.

AMS Subject Classification (1991)

Primary: 20H15
Secondary: 20F55


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