Introduction to Representations of Real Semisimple Lie Groups
by Matvei Libine
Publisher: arXiv 2012
Number of pages: 132
These are lecture notes for a one semester introductory course I gave at Indiana University. The goal was to make this exposition as clear and elementary as possible. A particular emphasis is given on examples involving SU(1,1).
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by F. Bruhat - Tata Institute of Fundamental Research
We consider some heterogeneous topics relating to Lie groups and the general theory of representations of locally compact groups. We have rigidly adhered to the analytic approach in establishing the relations between Lie groups and Lie algebras.
by Fiona Murnaghan - University of Toronto
Contents: Valuations and local fields; Smooth representations of locally compact totally disconnected groups; Haar measure, convolution, and characters of admissible representations; Induced representations - general properties; etc.
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Presents the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The text includes preliminaries that make the material accessible to anyone with basic knowledge of universal algebra.
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The purpose of these lectures is to describe a factorial correspondence between the theory of admissible representations for a complex semisimple Lie group and the theory of highest weight modules for a semisimple Lie algebra.