Marcelo Aguiar ; Carlos André ; Carolina Benedetti ; Nantel Bergeron ; Zhi Chen et al. - 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) - 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 ORCID4; 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 ORCID14; 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 ORCID18; Nathaniel Thiem 22; Vidya Venkateswaran 23; C. Ryan Vinroot 24; Ning Yan 25; Mike Zabrocki ORCID4

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.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: supercharacters, set partitions, symmetric functions in non-commuting variables, Hopf algebras,[INFO]Computer Science [cs],[MATH]Mathematics [math]
Funding:
    Source : OpenAIRE Graph
  • Funder: Natural Sciences and Engineering Research Council of Canada
  • Statistical Theory and Methodology; Funder: National Science Foundation; Code: 0804324
  • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641
  • FRG: Collaborative Research: Characters, Liftings, and Types: Investigations in p-adic Representation Theory; Funder: National Science Foundation; Code: 0854849
  • FRG: Collaborative Research: Characters, Liftings, and Types: Investigations in p-adic Representation Theory; Funder: National Science Foundation; Code: 0854893

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