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 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 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 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 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.