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

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

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

53 Citations (Scopus)


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
Pages (from-to)2310-2337
Number of pages28
JournalAdvances in Mathematics
Issue number4
Publication statusPublished - 1 Mar 2012

User-Defined Keywords

  • Supercharacters
  • Unipotent uppertriangular matrices
  • Symmetric functions in noncommuting variables
  • Finite fields
  • Combinatorial Hopf algebra


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