Notes On The Imprimitivity Theorem

Abstract

These notes were the basis of a course of (four) lectures given by the author at a Winter School on Group Representations and Function Theory conducted by the Indian Statistical Institute at Bangalore in October 1995. The author is particularly happy to be able to have these notes appear in a volume in honour of Professor K.R. Parthasarathy, since the author first learnt about the inducing construction and the imprimitivity theorem from his lecture notes which are referred to in the references. While there is nothing in these notes which is not already to be found in the lecture notes referred to above, it is hoped that these notes might serve some purpose as they restrict themselves to just these notions and a prospective reader who does not want to necessarily read about the mathematical foundations of quantum mechanics might be able to get directly to the imprimitivity theorem.