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 Thomas J. Enright - Tata Institute of Fundamental Research
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.
by Brian C. Hall - arXiv
An elementary introduction to Lie groups, Lie algebras, and their representations. Topics include definitions and examples of Lie groups and Lie algebras, the basics of representations theory, the Baker-Campbell-Hausdorff formula, and more.
by F. Bruhat - Tata Institute of Fundamental Research
The text covers the classical theory of valuated fields, results about representations of classical groups over a locally compact valuated field, and Dwork's proof of the rationality of the zeta function of an algebraic variety over a finite field.
by Peter Webb - University of Minnesota
The book is intended to be used as a learning tool by people who do not know the subject. It is intended to be appropriate for non-specialists in the area of representation theory, such as those whose primary interest is topology or combinatorics.