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 Fiona Murnaghan - University of Toronto
Contents: Representation Theory of Groups - Algebraic Foundations; Representations of Finite Groups; Representations of SL2(Fq); Representations of Finite Groups of Lie Type; Topological Groups, Representations, and Haar Measure; etc.
by Pavel Etingof, at al. - MIT
Representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics and quantum field theory.
by William Crawley-Boevey - University of Leeds
These are lectures on the symmetric group, the general linear group and invariant theory. The course covered as much of the classical theory as time allowed. The text requires some knowledge of rings and modules, character theory, affine varieties.
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.