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.
Read more about this topic: Complex Reflection Group
Famous quotes containing the words complex, reflection and/or groups:
“Power is not an institution, and not a structure; neither is it a certain strength we are endowed with; it is the name that one attributes to a complex strategical situation in a particular society.”
—Michel Foucault (1926–1984)
“The American, if he has a spark of national feeling, will be humiliated by the very prospect of a foreigner’s visit to Congress—these, for the most part, illiterate hacks whose fancy vests are spotted with gravy, and whose speeches, hypocritical, unctuous, and slovenly, are spotted also with the gravy of political patronage, these persons are a reflection on the democratic process rather than of it; they expose it in its process rather than of it; they expose it in its underwear.”
—Mary McCarthy (1912–1989)
“And seniors grow tomorrow
From the juniors today,
And even swimming groups can fade,
Games mistresses turn grey.”
—Philip Larkin (1922–1986)