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 1; Carlos André 2; Carolina Benedetti 3; Nantel Bergeron ORCID-iD3; Zhi Chen 3; Persi Diaconis 4; Anders Hendrickson 5; Samuel Hsiao 6; I. Martin Isaacs 7; Andrea Jedwab 8; Kenneth Johnson 9; Gizem Karaali 10; Aaron Lauve 11; Tung Le 12; Stephen Lewis ORCID-iD13; Huilan Li 14; Kay Magaard 15; Eric Marberg 16; Jean-Christophe Novelli 17; Amy Pang 18; Franco Saliola 19; Lenny Tevlin 20; Jean-Yves Thibon ORCID-iD17; Nathaniel Thiem 21; Vidya Venkateswaran 22; C. Ryan Vinroot 23; Ning Yan 24; Mike Zabrocki ORCID-iD3

  • 1 Department of Mathematics and Statistics [Texas Tech]
  • 2 Université de Lisbonne
  • 3 Department of Mathematics and Statistics [Toronto]
  • 4 Department of Statistics [Stanford]
  • 5 Concordia College [MN]
  • 6 Bard College
  • 7 University of Wisconsin-Madison
  • 8 University of Southern California
  • 9 Pennsylvania State University
  • 10 Pomona College
  • 11 Loyola University [Chicago]
  • 12 University of Aberdeen
  • 13 University of Washington [Seattle]
  • 14 Computer Science Department [Drexel]
  • 15 University of Birmingham [Birmingham]
  • 16 MIT Laboratory for Computer Science
  • 17 Laboratoire d'Informatique Gaspard-Monge
  • 18 Stanford University
  • 19 Laboratoire de combinatoire et d'informatique mathématique [Montréal]
  • 20 New York University [New York]
  • 21 Department of Mathematics, University of Colorado
  • 22 California Institute of Technology
  • 23 College of William and Mary [Williamsburg]
  • 24 Unknown

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: 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]
Funding:
    Source : OpenAIRE Graph
  • 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
  • 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

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 0712.1237
Source : ScholeXplorer IsRelatedTo DOI 10.37236/112
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0712.1237
  • 0712.1237
  • 10.37236/112
  • 10.37236/112
  • 10.48550/arxiv.0712.1237
Restricting supercharacters of the finite group of unipotent uppertriangular matrices

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