Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
Combinatorics
2012-01-24 v2 Representation Theory
Abstract
We identify 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 isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.
Keywords
Cite
@article{arxiv.1009.4134,
title = {Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras},
author = {Marcelo Aguiar and Carlos Andre and Carolina Benedetti and Nantel Bergeron and Zhi Chen and Persi Diaconis and Anders Hendrickson and Samuel Hsiao and I. Martin Isaacs and Andrea Jedwab and Kenneth Johnson and Gizem Karaali and Aaron Lauve and Tung Le and Stephen Lewis and Huilan Li and Kay Magaard and Eric Marberg and Jean-Christophe Novelli and Amy Pang and Franco Saliola and Lenny Tevlin and Jean-Yves Thibon and Nathaniel Thiem and Vidya Venkateswaran and C. Ryan Vinroot and Ning Yan and Mike Zabrocki},
journal= {arXiv preprint arXiv:1009.4134},
year = {2012}
}
Comments
To Appear in Advances in Mathematics (2012), 23 pages