Supercharacters, symmetric functions in noncommuting variables (extended abstract)
| Autor: | Andrea Jedwab, Mike Zabrocki, Eric Marberg, Persi Diaconis, Amy Pang, Carlos A. M. André, Samuel K. Hsiao, Marcelo Aguiar, Gizem Karaali, Lenny Tevlin, Vidya Venkateswaran, Zhi Chen, Carolina Benedetti, I. Martin Isaacs, Stephen Lewis, Franco Saliola, Huilan Li, Nathaniel Thiem, Kenneth A. Johnson, Jean-Christophe Novelli, Aaron Lauve, C. Ryan Vinroot, Nantel Bergeron, Jean-Yves Thibon, Anders O.F. Hendrickson, Tung Le, Kay Magaard, Ning Yan |
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| Přispěvatelé: | Department of Mathematics and Statistics [Texas Tech], Texas Tech University [Lubbock] (TTU), Université de Lisbonne, Department of Mathematics and Statistics [Toronto], York University [Toronto], Department of Statistics [Stanford], Stanford University, Concordia College [MN], Bard College, University of Wisconsin-Madison, University of Southern California (USC), Pennsylvania State University (Penn State), Penn State System, Pomona College, Loyola University [Chicago], University of Aberdeen, University of Washington [Seattle], Computer Science Department [Drexel], Drexel University, University of Birmingham [Birmingham], MIT Laboratory for Computer Science, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Laboratoire de combinatoire et d'informatique mathématique [Montréal] (LaCIM), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Université du Québec à Montréal = University of Québec in Montréal (UQAM), New York University [New York] (NYU), NYU System (NYU), Department of Mathematics, University of Colorado, University of Colorado [Boulder], California Institute of Technology (CALTECH), College of William and Mary [Williamsburg] (WM), Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel, Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Pure mathematics
Class (set theory) General Computer Science Field (mathematics) 0102 computer and information sciences [MATH] Mathematics [math] Unipotent [INFO] Computer Science [cs] 01 natural sciences Theoretical Computer Science Mathematics::Quantum Algebra Discrete Mathematics and Combinatorics [INFO]Computer Science [cs] 0101 mathematics [MATH]Mathematics [math] Ring of symmetric functions Mathematics Group (mathematics) 010102 general mathematics supercharacters Hopf algebra Symmetric function Algebra Finite field set partitions 010201 computation theory & mathematics Hopf algebras symmetric functions in non-commuting variables |
| Zdroj: | Scopus-Elsevier Discrete Mathematics and Theoretical Computer Science Discrete Mathematics and Theoretical Computer Science (DMTCS) 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.3-14 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.3-14, ⟨10.46298/dmtcs.2967⟩ |
| ISSN: | 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.2967⟩ |
| Popis: | 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. Nous montrons que deux structures en apparence bien différentes peuvent être identifiées: les super-caractères, qui sont un outil commode pour faire de l'analyse de Fourier sur le groupe des matrices unipotentes triangulaires supérieures à coefficients dans un corps fini, et l'anneau des fonctions symétriques en variables non-commutatives. Ces deux structures sont des algèbres de Hopf isomorphes. Cette identification permet de traduire dans une structure les dévelopements conçus pour l'autre, et suggère de nombreux exemples dans le domaine nouveau des algèbres de Hopf combinatoires. |
| Databáze: | OpenAIRE |
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