A complex reflection is a linear transformation which fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or arrangement of mirrors. This book gives a complete classification of all groups of transformations of n-dimensional complex space which are generated by complex reflections, using the method of line systems. In particular: irreducible groups are studied in detail, and are identified with finite linear groups; reflection subgroups of reflection groups are completely classified; the theory of eigenspaces of elements of reflection groups is discussed fully; an appendix outlines links to representation theory, topology and mathematical physics. Containing over 100 exercises ranging in difficulty from elementary to research level, this book is ideal for honours and graduate students, or for researchers in algebra, topology and mathematical physics.
- ISBN13 9780521749893
- Publish Date 13 August 2009 (first published 1 January 2009)
- Publish Status Active
- Out of Print 10 December 2021
- Publish Country GB
- Imprint Cambridge University Press
- Format Paperback (US Trade)
- Pages 302
- Language English