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Finite Unitary Reflection Groups

delete2018-11-20
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DOI:10.4153/cjm-1954-028-3delete
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Any finite group of linear transformations onnvariables 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 Unofndimensions, in which the points are specified by complex vectors withncomponents, and the distance between two points is the norm of the difference between their corresponding vectors.
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