Discrete Mathematics & Theoretical Computer Science (Jan 2011)
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 Pang,
- Franco Saliola,
- Lenny Tevlin,
- Jean-Yves Thibon,
- Nathaniel Thiem,
- Vidya Venkateswaran,
- C. Ryan Vinroot,
- Ning Yan,
- Mike Zabrocki
Affiliations
- Marcelo Aguiar
- Department of Mathematics and Statistics [Texas Tech]
- Carlos André
- Université de Lisbonne
- Carolina Benedetti
- Department of Mathematics and Statistics [Toronto]
- Nantel Bergeron
- ORCiD
- Department of Mathematics and Statistics [Toronto]
- Zhi Chen
- Department of Mathematics and Statistics [Toronto]
- Persi Diaconis
- Department of Statistics [Stanford]
- Anders Hendrickson
- Concordia College [MN]
- Samuel Hsiao
- Bard College
- I. Martin Isaacs
- University of Wisconsin-Madison
- Andrea Jedwab
- University of Southern California
- Kenneth Johnson
- Pennsylvania State University
- Gizem Karaali
- Pomona College
- Aaron Lauve
- Loyola University [Chicago]
- Tung Le
- University of Aberdeen
- Stephen Lewis
- ORCiD
- University of Washington [Seattle]
- Huilan Li
- Computer Science Department [Drexel]
- Kay Magaard
- University of Birmingham [Birmingham]
- Eric Marberg
- MIT Laboratory for Computer Science
- Jean-Christophe Novelli
- Laboratoire d'Informatique Gaspard-Monge
- Amy Pang
- Stanford University
- Franco Saliola
- Laboratoire de combinatoire et d'informatique mathématique [Montréal]
- Lenny Tevlin
- New York University [New York]
- Jean-Yves Thibon
- ORCiD
- Laboratoire d'Informatique Gaspard-Monge
- Nathaniel Thiem
- Department of Mathematics, University of Colorado
- Vidya Venkateswaran
- California Institute of Technology
- C. Ryan Vinroot
- College of William and Mary [Williamsburg]
- Ning Yan
- Unknown
- Mike Zabrocki
- ORCiD
- Department of Mathematics and Statistics [Toronto]
- DOI
- https://doi.org/10.46298/dmtcs.2967
- Journal volume & issue
-
Vol. DMTCS Proceedings vol. AO,...,
no. Proceedings
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.
Keywords
- supercharacters
- set partitions
- symmetric functions in non-commuting variables
- hopf algebras
- [info] computer science [cs]
- [math] mathematics [math]
