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Graduate Seminar

Jacob Davis
Carnegie Mellon University
Title: Representation theory

Abstract: Representation theory is a major branch of algebra, that uses vectors and matrices to develop a better understanding of the properties of more abstract algebraic structures such as groups; in this talk we will be looking at its applications to finite groups. A *representation* of a group G is a homomorphism from the group to GL_n(C), the space of invertible n-by-n complex matrices. All representations can be constructed from certain *irreducible* representations, and we will be interested in identifying all of the irreducible representations of a given finite group.

Each representation then has a *character*, which permits us to construct for each group a *character table* of the characters of all its irreducible representations. In addition to being entertaining, these character tables have many important properties, and provide a lot of information about the original group. We will see (at least the statement of) an application of this in Burnside's Theorem, which is an important first step in the classification of finite simple groups.

Date: Thursday, October 3, 2013
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell