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:
“When distant and unfamiliar and complex things are communicated to great masses of people, the truth suffers a considerable and often a radical distortion. The complex is made over into the simple, the hypothetical into the dogmatic, and the relative into an absolute.”
—Walter Lippmann (1889–1974)
“Fanny was not there! How she would have enjoyed the scene.... I could not but think of her, and in spite of my efforts to prevent, the unbidden tear would flow. Alas! I cannot feel the satisfaction some appear to do in the reflection that her eyes beheld the scene from the other world.”
—Rutherford Birchard Hayes (1822–1893)
“In America every woman has her set of girl-friends; some are cousins, the rest are gained at school. These form a permanent committee who sit on each other’s affairs, who “come out” together, marry and divorce together, and who end as those groups of bustling, heartless well-informed club-women who govern society. Against them the Couple of Ehepaar is helpless and Man in their eyes but a biological interlude.”
—Cyril Connolly (1903–1974)