Multipliers and induced representations of locally compact groups

Abstract

In Chapter 1, we have given a brief account of measure theory on locally compact groups. We have defined unitary representations and have given their elementary properties. G-spaces and semi-direct products are also briefly discussed. Section 2.1 of Chapter 2 describes an application of the imprimitivity theorem to quantum mechanics. In section 2.2 induced representations for locally compact groups are discussed. The inducing construction on the spaces [equations] is described and it is shown that the resulting induced representations are unitaryequivalent. In section 2.3 and 2.4 Mackey's imprimitivity Theorem is stated and a recent proof is given. In Chapter 3, physical considerations leading to the concept of projective representations are discussed. Borel multipliers on locally compact groups are defined and some examples given. In Section 4.1 of Chapter 4 gauge transformations andgauge group are briefly discussed. In Section 4.2 the inducing construction on the Mackey Space [equation] is defined. It is shown that the induced representation on the space is unitary equivalent to it for any choice of Borel section [equation]. In Section 4.3 ageneralization of Stone-von Neumann theorem is given.