CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Supercharacter Theories and Schur Rings Justin Keller, CU
October 30 - November 6, 2012 Math 350 2-3pm	Abstract We define the notion of a supercharacter theory (SCT) for an arbitrary finite group and view each SCT as a coarsening or approximation of the usual character theory of the group. Generalizing the relationship between the center of the group algebra and its character theory, we describe how certain subalgebras (Schur rings) of the group algebra play an analogous role for SCTs. In this way, Schur rings can be viewed as an approximate center for the group algebra, and as a tool for finding and understanding SCTs. The goal will be to provide a foundation and motivating example (the group algebra) for the following talk, which will introduce the notion of a Schur ring in the setting of Hopf algebras.

Supercharacter Theories and Schur Rings

Justin Keller, CU

October 30 - November 6, 2012

Math 350

2-3pm

Abstract

We define the notion of a supercharacter theory (SCT) for an arbitrary finite group and view each SCT as a coarsening or approximation of the usual character theory of the group. Generalizing the relationship between the center of the group algebra and its character theory, we describe how certain subalgebras (Schur rings) of the group algebra play an analogous role for SCTs. In this way, Schur rings can be viewed as an approximate center for the group algebra, and as a tool for finding and understanding SCTs. The goal will be to provide a foundation and motivating example (the group algebra) for the following talk, which will introduce the notion of a Schur ring in the setting of Hopf algebras.