CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Supercharacters and combinatorial Hopf algebras Nat Thiem, CU
August 31 and September 7, 2010 Math 350 2-3pm	Abstract At a recent AIM workshop, the participants found a remarkable connection between two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are Hopf isomorphic. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras. This talk will be in two parts: (1) I will give an introduction to combinatorial Hopf algebras with our favorite examples (2) I will describe supercharacters and how they connect up to one of our favorite Hopf algebras.

Supercharacters and combinatorial Hopf algebras

Nat Thiem, CU

August 31 and September 7, 2010

Math 350

2-3pm

Abstract

At a recent AIM workshop, the participants found a remarkable connection between two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are Hopf isomorphic. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras. This talk will be in two parts: (1) I will give an introduction to combinatorial Hopf algebras with our favorite examples (2) I will describe supercharacters and how they connect up to one of our favorite Hopf algebras.