Lectures on local Lie groups and their representations [MatSciRep:25]

Abstract

A series of 24 lectures delivered at the Institute on this topic, was aimed to provide a fairly extensive working knowledge of the 'local Lie groups and their representations' for the audience group of physicists - in particular for students of Quantum mechanics. The series roughly grouped into three parts. Part I deals with the general theory of abstract local lie groups and associated transformation groups, then introduces Lie Algebra. Part II deals with construction of irreducible representations of Lie Algebra, and semi-simple lie groups as per its definitions in Part I. Ordinary Functional Analysis, theory of Linear Operators(Matrices) on vector and metric spaces are applied in these two Parts. Part III deals with a particular problem in the Representation theory of Part II, ie., the problem of constructing all the independent invariants for any given Lie group. All the results quoted in this series can be proved with elementary mathematical methods. The questions asked during these lecture series and their relevant answers have been included as part of the text in the Report.