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: Contribution to conferencePaper

1 Scopus citations

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 (US)
Pages3-14
Number of pages12
StatePublished - Dec 1 2011
Event23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 - Reykjavik, Iceland
Duration: Jun 13 2011Jun 17 2011

Conference

Conference23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11
CountryIceland
CityReykjavik
Period6/13/116/17/11

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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    Aguiar, M., André, C., Benedetti, C., Bergeron, N., Chen, Z., Diaconis, P., Hendrickson, A., Hsiao, S., Isaacs, I. M., Jedwab, A., Johnson, K., Karaali, G., Lauve, A., Le, T., Lewis, S., Li, H., Magaard, K., Marberg, E., Novelli, J. C., ... Zabrocki, M. (2011). Supercharacters, symmetric functions in noncommuting variables, extended abstract. 3-14. Paper presented at 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11, Reykjavik, Iceland.