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Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

Authors :
Carolina Benedetti
Samuel K. Hsiao
Nantel Bergeron
Carlos A. M. André
I. Martin Isaacs
Gizem Karaali
Ning Yan
Persi Diaconis
Anders O.F. Hendrickson
Huilan Li
Tung Le
Nathaniel Thiem
Jean-Yves Thibon
Marcelo Aguiar
Zhi Chen
Vidya Venkateswaran
Amy Pang
Franco Saliola
Aaron Lauve
Kenneth A. Johnson
Kay Magaard
Mike Zabrocki
Andrea Jedwab
Stephen Lewis
Jean-Christophe Novelli
C. Ryan Vinroot
Lenny Tevlin
Eric Marberg
Department of Mathematics and Statistics [Texas Tech]
Texas Tech University [Lubbock] (TTU)
Department of Mathematics and Statistics [Toronto]
York University [Toronto]
Department of Statistics [Stanford]
Stanford University
Department of Natural Sciences
University of Houston
Department of Mathematics [Austin]
University of Texas at Austin [Austin]
Gastroenterology
Derriford Hospital
Laboratoire d'Informatique Gaspard-Monge (LIGM)
Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)
Source :
Advances in Mathematics, Advances in Mathematics, Elsevier, 2011, 229, pp.2310-2337. ⟨10.1016/j.aim.2011.12.024⟩
Publisher :
Elsevier Inc.

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.<br />Comment: To Appear in Advances in Mathematics (2012), 23 pages

Details

Language :
English
ISSN :
00018708 and 10902082
Issue :
4
Database :
OpenAIRE
Journal :
Advances in Mathematics
Accession number :
edsair.doi.dedup.....be8edf90db13b5010a4bd4ece93da33c
Full Text :
https://doi.org/10.1016/j.aim.2011.12.024