CU Algebraic Lie Theory Seminar

Supercharacters and the combinatorics of set-partitions (2 parts)

Nat Thiem, CU

September 24 and October 1, 2009
2-3pm
Math 220

Abstract

The two parts of this talk are as follows:

In the first talk, we will review the concept of a supercharacter theory with an eye towards applying these ideas to algebraic structures that are not finite groups. In particular, there is much to be explored in the realm of finite dimensional algebras and infinite groups.

In the second talk, we will explore the combinatorics of set-partitions via a supercharacter theory of the group of finite unipotent upper-triangular matrices. This classical example was the original motivation for defining supercharacters, and the resulting combinatorics is analogous to the integer partitions in the representation theory of the symmetric group. By studying the decomposition of restrictions and tensor products of supercharacters into supercharacters, this talk finds a surprising analogue to the combinatorics of the Littlewood--Richardson coefficients of the symmetric group. Joint with S. Lewis.