@article{303b94cbf657473f90399d2ff603a54a,
title = "Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras",
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.",
author = "Marcelo Aguiar and Carlos Andr{\'e} and Carolina Benedetti and Nantel Bergeron and Zhi Chen and Persi Diaconis and Anders Hendrickson and Samuel Hsiao and Isaacs, {I. Martin} 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 Novelli, {Jean Christophe} and Amy Pang and Franco Saliola and Lenny Tevlin and Thibon, {Jean Yves} and Nathaniel Thiem and Vidya Venkateswaran and Vinroot, {C. Ryan} and Ning Yan and Mike Zabrocki",
note = "Funding Information: diaconis@math.stanford.edu (P. Diaconis), ahendric@cord.edu (A. Hendrickson), hsiao@bard.edu (S. Hsiao), isaacs@math.wisc.edu (I.M. Isaacs), jedwab@usc.edu (A. Jedwab), kwj1@psu.edu (K. Johnson), gizem.karaali@pomona.edu (G. Karaali), lauve@math.luc.edu (A. Lauve), lttung96@yahoo.com (T. Le), stedalew@u.washington.edu (S. Lewis), huilan.li@gmail.com (H. Li), k.magaard@bham.ac.uk (K. Magaard), emarberg@math.mit.edu (E. Marberg), novelli@univ-mlv.fr (J.-C. Novelli), amypang@stanford.edu (A. Pang), saliola@gmail.com (F. Saliola), ltevlin@nyu.edu (L. Tevlin), jyt@univ-mlv.fr (J.-Y. Thibon), thiemn@colorado.edu (N. Thiem), vidyav@caltech.edu (V. Venkateswaran), vinroot@math.wm.edu (C.R. Vinroot), ning.now@gmail.com (N. Yan), zabrocki@mathstat.yorku.ca (M. Zabrocki). 1 Supported by NSF DMS-1001935. 2 Supported by CRC and Beca Mazda. 3 Supported by CRC and NSERC. 4 Supported by NSF DMS-0804324. 5 Supported by NSF DMS 07-01291. 6 Supported by NSA H98230-10-1-0362. 7 Supported by NSF DMS-0854893. 8 Supported by NSF DMS-0652641. 9 Supported by NDSEG Fellowship. 10 Supported by CRC. 11 Supported by NSF DMS-0854849. 12 Supported by NSERC.",
year = "2012",
month = mar,
day = "1",
doi = "10.1016/j.aim.2011.12.024",
language = "English (US)",
volume = "229",
pages = "2310--2337",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
number = "4",
}