Supercharacters, symmetric functions in noncommuting variables, extended abstract

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 PANGFranco Saliola, Lenny Tevlin, Jean Yves Thibon, Nathaniel Thiem, Vidya Venkateswaran, C. Ryan Vinroot, Ning Yan, Mike Zabrocki

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

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.
Original languageEnglish
Title of host publication23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
PublisherMaison de l'informatique et des mathematiques discretes
Pages3-14
Number of pages12
DOIs
Publication statusPublished - 1 Jan 2011

Publication series

NameDiscrete Mathematics & Theoretical Computer Science Proceedings
ISSN (Print)1365-8050

User-Defined Keywords

  • supercharacters
  • set partitions
  • symmetric functions in non-commuting variables
  • Hopf algebras

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