Coupling, subduction and induction transformations for group representations

Abstract

The basis of a representation space of any group may be chosen according to its decomposition into representations of the group and a subgroup chain. Coupling, recoupling, subduction and resubduction factors are each shown to arise as a result of Schur's lemmas and a particular group-subgroup structure. When induction and Mackey's subgroup theorem are considered new transformation factors occur, those of induction and reinduction. Key properties of these factors are given, together with their relationship with double coset matrix elements.