New Methods for Reduction of Group Representations Using an Extension of Schur's Lemma

Abstract

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.