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On Counting Types of Symmetries in Finite Unitary Reflection Groups

Published online by Cambridge University Press:  20 November 2018

C. L. Morgan
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Let K be a field of characteristic zero. Let V be an n-dimensional vector space over K. A linear automorphism of V is said to be of type i if it leaves fixed a subspace of dimension i. A reflection is a linear automorphism of type n − 1 which has finite order. A finite reflection group is a finite group of linear automorphisms which is generated by reflections. These groups are especially interesting because the full group of symmetries of a regular poly tope is always a finite reflection group. There is also a strong connection between these groups and Lie groups.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 252 - 254
Copyright
Copyright © Canadian Mathematical Society 1979

References

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3. Solomon, L., Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), 57–64.Google Scholar