Supercharacters, symmetric functions in noncommuting variables (extended abstract)
Marcelo Aguiar (1), Carlos André (2) (3) (4), Carolina Benedetti (5), Nantel Bergeron (5), Zhi Chen (5), Persi Diaconis (6), Anders Hendrickson (7), Samuel Hsiao (8), I. Martin Isaacs (9), Andrea Jedwab (10), Kenneth Johnson (11) (12), Gizem Karaali (13), Aaron Lauve (14), Tung Le (15), Stephen Lewis (16), Huilan Li (17), Kay Magaard (18), Eric Marberg (19), Jean-Christophe Novelli (20), Amy Pang (21), Franco Saliola (22), Lenny Tevlin (23), Jean-Yves Thibon (20), Nathaniel Thiem (24), Vidya Venkateswaran (25), C. Ryan Vinroot (26), Ning Yan (27), Mike Zabrocki (5)
(1) Department of Mathematics and Statistics [Texas Tech]
(2) Université de Lisbonne
(3) Universidade de Lisboa = University of Lisbon = Université de Lisbonne
(4) Universidade de Lisboa = University of Lisbon = Université de Lisbonne [Lisboa]
(5) Department of Mathematics and Statistics [Toronto]
(6) Department of Statistics [Stanford]
(7) Concordia College [MN]
(8) Bard College
(9) University of Wisconsin-Madison
(10) University of Southern California
(11) Pennsylvania State University
(12) Pennsylvania State University [State College, PA]
(13) Pomona College
(14) Loyola University [Chicago]
(15) University of Aberdeen
(16) University of Washington [Seattle]
(17) Computer Science Department [Drexel]
(18) University of Birmingham [Birmingham]
(19) MIT Laboratory for Computer Science
(20) Laboratoire d'Informatique Gaspard-Monge
(21) Stanford University
(22) Laboratoire de combinatoire et d'informatique mathématique [Montréal]
(23) New York University [New York]
(24) Department of Mathematics, University of Colorado
FRG: Collaborative Research: Characters, Liftings, and Types: Investigations in p-adic Representation Theory
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Supercharacters, symmetric functions in noncommuting variables (extended abstract)
Marcelo Aguiar (1), Carlos André (2) (3) (4), Carolina Benedetti (5), Nantel Bergeron (5), Zhi Chen (5), Persi Diaconis (6), Anders Hendrickson (7), Samuel Hsiao (8), I. Martin Isaacs (9), Andrea Jedwab (10), Kenneth Johnson (11) (12), Gizem Karaali (13), Aaron Lauve (14), Tung Le (15), Stephen Lewis (16), Huilan Li (17), Kay Magaard (18), Eric Marberg (19), Jean-Christophe Novelli (20), Amy Pang (21), Franco Saliola (22), Lenny Tevlin (23), Jean-Yves Thibon (20), Nathaniel Thiem (24), Vidya Venkateswaran (25), C. Ryan Vinroot (26), Ning Yan (27), Mike Zabrocki (5)
(1) Department of Mathematics and Statistics [Texas Tech]
(2) Université de Lisbonne
(3) Universidade de Lisboa = University of Lisbon = Université de Lisbonne
(4) Universidade de Lisboa = University of Lisbon = Université de Lisbonne [Lisboa]
(5) Department of Mathematics and Statistics [Toronto]
(6) Department of Statistics [Stanford]
(7) Concordia College [MN]
(8) Bard College
(9) University of Wisconsin-Madison
(10) University of Southern California
(11) Pennsylvania State University
(12) Pennsylvania State University [State College, PA]
(13) Pomona College
(14) Loyola University [Chicago]
(15) University of Aberdeen
(16) University of Washington [Seattle]
(17) Computer Science Department [Drexel]
(18) University of Birmingham [Birmingham]
(19) MIT Laboratory for Computer Science
(20) Laboratoire d'Informatique Gaspard-Monge
(21) Stanford University
(22) Laboratoire de combinatoire et d'informatique mathématique [Montréal]
(23) New York University [New York]
(24) Department of Mathematics, University of Colorado
(25) California Institute of Technology
(26) College of William and Mary [Williamsburg]
(27) Unknown
Abstract
English
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.
French
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.
Keywords
[INFO]Computer Science [cs]
[MATH]Mathematics [math]
supercharacters
set partitions
symmetric functions in non-commuting variables
Hopf algebras
Cited by
Source: OpenCitations
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