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 I
Sep. 07, 2010 2pm (MATH 350)
Lie Theory
Nat Thiem (CU)
X
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 II
Sep. 21, 2010 2pm (MATH 350)
Lie Theory
Jacob Harper (CU)
X
This talk will be split into two parts. In the first part I will describe a hypersimplex and go over concepts of Coxeter groups and topology in order to get a better understanding of this polytope. In the second talk I will describe a matching on the face lattice of a hypersimplex and use discrete Morse theory to classify all subcomplexes whose reduced homology groups are concentrated in a single degree. These homology groups support a natural action of the symmetric group and I will finish my talk by describing the characters that this action produces.
Homology representations arising from a hypersimplex I
Sep. 28, 2010 2pm (MATH 350)
Lie Theory
Jacob Harper (CU)
X
This talk will be split into two parts. In the first part I will describe a hypersimplex and go over concepts of Coxeter groups and topology in order to get a better understanding of this polytope. In the second talk I will describe a matching on the face lattice of a hypersimplex and use discrete Morse theory to classify all subcomplexes whose reduced homology groups are concentrated in a single degree. These homology groups support a natural action of the symmetric group and I will finish my talk by describing the characters that this action produces.
Homology representations arising from a hypersimplex II
Supercharacters and combinatorial Hopf algebras I