Finite Unitary Reflection Groups
G. C. Shephard, J. A. Todd
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Source: Crossref
Published: Jan 1, 1954
DOI: 10.4153/cjm-1954-028-3
Open original source ↗Source abstract
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 U n 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.
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