Marcelo Aguiar ; Carlos André ; Carolina Benedetti ; Nantel Bergeron ; Zhi Chen et al.
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Supercharacters, symmetric functions in noncommuting variables (extended abstract)
dmtcs:2967 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
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https://doi.org/10.46298/dmtcs.2967
Supercharacters, symmetric functions in noncommuting variables (extended abstract)
Authors: 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
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.