Introduction to Representation Theory
by Pavel Etingof, at al.
Publisher: MIT 2009
Number of pages: 99
Very roughly speaking, 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.
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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 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 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.