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)Conference paper
Authors: Marcelo Aguiar 1; Carlos André 2,3; Carolina Benedetti 4; Nantel Bergeron 4; Zhi Chen 4; Persi Diaconis 5; Anders Hendrickson 6; Samuel Hsiao 7; I. Martin Isaacs 8; Andrea Jedwab 9; Kenneth Johnson 10; Gizem Karaali 11; Aaron Lauve 12; Tung Le 13; Stephen Lewis 14; Huilan Li 15; Kay Magaard 16; Eric Marberg 17; Jean-Christophe Novelli 18; Amy Pang 19; Franco Saliola 20; Lenny Tevlin 21; Jean-Yves Thibon 18; Nathaniel Thiem 22; Vidya Venkateswaran 23; C. Ryan Vinroot 24; Ning Yan 25; Mike Zabrocki 4
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.