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Discrete Mathematics & Theoretical Computer Science |
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
3; 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 13; 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 17; Nathaniel Thiem 21; Vidya Venkateswaran 22; C. Ryan Vinroot 23; Ning Yan 24; Mike Zabrocki 3
- 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.
- Source : OpenAIRE Graph
- 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: 0854893
- 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: 0854849