Well-generated Complex Reflection Groups
An irreducible complex reflection group of rank is generated by or by reflections. It is said to be well-generated if it is generated by reflections ; it is proved that this is equivalent to the property for all . For irreducible well-generated complex reflection groups, the Coxeter number is defined to be the largest degree, . A reducible complex reflection group is said to be well-generated if it is a product of irreducible well-generated complex reflection groups. Any finite real reflection group is well-generated.
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