New Methods for Reduction of Group Representations Using an Extension of Schur's Lemma
John R. Gabriel · Journal of Mathematical Physics · 1964
The generators of the group or group algebra are used in an analog of the Lie-Cartan method, which can be applied to finite or infinite groups. This gives a mean for reduction of an arbitrary group representation, using only the matrix representatives of the generators. It is a set of algorithms using pivotal condensation and can easily be coded as a digital computer program. Connections with Lie-Cartan theory are suggested, the reduction of the symmetric group discussed, and methods for the reduction of representations of the n × n unitary, orthogonal, and proper orthogonal groups suggested.