Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-23T14:04:38.528Z Has data issue: false hasContentIssue false
  • English
  • Français

On Counting Types of Symmetries in Finite Unitary Reflection Groups

Published online by Cambridge University Press:  20 November 2018

C. L. Morgan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

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

1. Coxeter, H. S. M., Regular complex polytopes, (Cambridge University Press, Cambridge, 1974).Google Scholar
2. Shephard, G. C. and Todd, J. A., Finite unitary reflection groups, Canadian J. Math. 6 (1954), 274–304.Google Scholar
3. Solomon, L., Invariants of finite reflection groups, Nagoya Math. J. 22 (1963), 57–64.Google Scholar