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Elsevier, Advances in Mathematics, 4(229), p. 2310-2337, 2012

DOI: 10.1016/j.aim.2011.12.024

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

Journal article published in 2011 by Marcelo Aguiar, Carlos A. M. Andre, Carolina Benedetti, Nantel Bergeron ORCID, Zhi Chen, Persi W. Diaconis, Anders O. F. Hendrickson, Samuel Hsiao, I. Martin Isaacs, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le and other authors.
This paper is available in a repository.
This paper is available in a repository.

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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.