Group representations on Hilbert bundles. I (Q1072165)

Vector bundles are of interest to the analyst because vector-valued functions may be viewed as cross-sections of vector bundles. Fibre bundles are of interest to the topologist because they generalize the notion of the product, and admit of the lifting of homotopies. The interplay of these features accounts for the prominent position they occupy in mathematics. It would, therefore, be natural to study fibre- preserving actions of groups on vector bundles. In these lectures we discuss the continuous actions of groups on bundles of Hilbert spaces, or briefly, Hilbert bundles. The motiviation for this study came from theoretical physics. The demands of the latter are concreteness, rather than generality, and this is reflected in our treatment.