Covariant representations in a fibre bundle framework
Two kinds or representations of an analytic semidirect product G of a Lie group K by an abelian Lie kernel N are studied in the present paper within a unifying fibre bundle approach. These are the representations induced (in Mackey's sense) by strongly continuous unitary representations of the isotropy group \(G_{\chi_ 0}\) of a character \(\chi_ 0\) of N (the canonical representations of G) and those induced by representations of K (the covariant representations of G). A relationship between both types of representations is established which allows a selection of irreducible covariant representations in two different ways. This result is then applied to the Poincaré group.
scientific article; zbMATH DE number 3998111
scientific article