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)

Authors: Marcelo Aguiar ; Carlos André ; Carolina Benedetti ; Nantel Bergeron ORCID-iD; 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 ORCID-iD

    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.

    https://doi.org/10.46298/dmtcs.2967
    Source : oai:HAL:hal-01336771v1
    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]
    Fundings :
      Source : OpenAIRE Research Graph
    • FRG: Collaborative Research: Characters, Liftings, and Types: Investigations in p-adic Representation Theory; Funder: National Science Foundation; Code: 0854849
    • Statistical Theory and Methodology; Funder: National Science Foundation; Code: 0804324
    • FRG: Collaborative Research: Characters, Liftings, and Types: Investigations in p-adic Representation Theory; Funder: National Science Foundation; Code: 0854893
    • Funder: Natural Sciences and Engineering Research Council of Canada
    • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641

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