# Supercharacters and combinatorial Hopf algebras

May 17 to May 21, 2010

at the

American Institute of Mathematics, San Jose, 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
by  J. L. Brumbaugh, Madeleine Bulkow, Patrick S. Fleming, Luis Alberto Garcia, Stephan Ramon Garcia, Gizem Karaali, Matt Michal, Hong Suh and Andrew P. Turner,  J. Number Theory 144 (2014), 151-175  MR3239156
Expansion of k-Schur functions for maximal k-rectangles within the affine nilCoxeter algebra
by  Chris Berg, Nantel Bergeron, Hugh Thomas, and Mike Zabrocki
On the character degrees of Sylow $p$-subgroups of Chevalley group of type $E(p^f)$
by  Tung Le and Kay Magaard,  Forum Math. 27 (2015), no. 1, 1-55  MR3334053
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
by  Marcelo Aguiar, Carlos Andre, Carolina Benedetti, Nantel Bergeron, Zhi Chen, Persi Diaconis, Anders Hendrickson, Samuel Hsiao, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le, Stephen Lewis, Huilan Li, Kay Magaard, Eric Marberg, Jean-Christophe Novelli, Amy Pang, Franco Saliola, Lenny Tevlin, Jean-Yves Thibon, Nathaniel Thiem, Vidya Venkateswaran, C. Ryan Vinroot, Ning Yan, and Mike Zabrocki