MA 765 - Representation Theory (Spring
2014)
Course by Uwe Nagel
at the University of Kentucky.
Overview
Schedule
MWF 11:00 - 11:50, FB 213.
Material
Representation Theory is the study of the ways a given group acts linearly on vector spaces. Since group actions are ubiquitous in mathematics, methods and results of representation theory are used in many areas, including algebra, combinatorics, and geometry.
We will begin by discussing representations of finite groups, in particular of the symmetric group. Then the focus will turn to Lie groups and Lie algebras and the classical (matrix) groups. The theory will be illustrated by many examples.
The course will be as self-contained as possible though some
familiarity with the ring-theoretic concepts of a first year
graduate Algebra course is preferable. The basic reference for the
course will be the book by Fulton and Harris.
CONTENTS:
1. Representations: Definitions and Examples
2. Complete Reducibility
3. Some Multilinear Algebra
4. Character Theory
5. Induced Representations
6. Representations and Group Algebras
7. Irreducible Representations of a Symmetric Group
- W. Fulton, J. Harris, Representation theory.
- C. W. Curtis, I. Reiner, Representation theory of finite groups and associative algebras.
- J. E. Humphreys, Introduction to Lie algebras and representation theory.
- J-P. Serre, Linear representations of finite groups.
- H. Weyl, Classical groups.