Supercharacters and combinatorial Hopf algebras

May 17 to May 21, 2010

at the

American Institute of Mathematics, Palo Alto, California

organized by

Nantel Bergeron, Persi Diaconis, Jean-Yves Thibon, and Nathaniel Thiem

Original Announcement

This workshop will bring together experts in the emerging area of supercharacter theory and experts in Hopf algebras. Super characters/classes are certain unions of irreducible characters/conjugacy classes which fit together to give a rich, new combinatorial structure that allows analysis for previously intractable problems such as the the group of upper triangular matrices with coefficients in a finite field Hopf algebras have given a useful framework for studying the representation theory of towers of algebras, following the classical relationship between the representation theory of the symmetric group and the ring of symmetric functions. Recent work has suggested that similar noncommutative Hopf algebraic structures might exist for super-representation theories. In particular, this workshop will investigate the case of finite groups of unipotent upper-triangular matrices.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:
Supercharacters, exponential sums, and the uncertainty principle
Expansion of k-Schur functions for maximal k-rectangles within the affine nilCoxeter algebra
On the character degrees of Sylow $p$-subgroups of Chevalley group of type $E(p^f)$
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras