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Finite Unitary Reflection Groups

Published online by Cambridge University Press:  20 November 2018

G. C. Shephard
Affiliation:
University of Birmingham
J. A. Todd
Affiliation:
University of Cambridge
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Extract

Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of unitary transformations (5, p. 257). Such a group may be thought of as a group of congruent transformations, keeping the origin fixed, in a unitary space Un of n dimensions, in which the points are specified by complex vectors with n components, and the distance between two points is the norm of the difference between their corresponding vectors.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1954

References

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