Lectures on Representation Theory and Invariant Theory
by William Crawley-Boevey
Publisher: University of Leeds 1990
Number of pages: 77
These are the notes for a lecture course on the symmetric group, the general linear group and invariant theory. The aim of the course was to cover as much of the beautiful classical theory as time allowed. The result is a text which requires no previous knowledge beyond a smattering of rings and modules, character theory, and affine varieties.
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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 Peter Jipsen, Henry Rose - Springer
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.
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 Matvei Libine - arXiv
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).