Supercharacters, symmetric functions in noncommuting variables (extended abstract)

Supercharacters, symmetric functions in noncommuting variables (extended 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 isomor...

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Bibliographic Details
Main Authors: Marcelo Aguiar, Carlos André, 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, Mike Zabrocki
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2011-01-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
supercharacters
set partitions
symmetric functions in non-commuting variables
hopf algebras
[info] computer science [cs]
[math] mathematics [math]
Online Access:https://dmtcs.episciences.org/2967/pdf
Description
Summary: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.
ISSN:1365-8050

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