Supercharacters, Symmetric Functions in Noncommuting Variables, and Related Hopf Algebras
Document Type
Article
Department
Mathematics (Pomona)
Publication Date
2012
Keywords
supercharacters, unipotent uppertriangular matrices, symmetric functions in noncommuting variables, finite fields, combinatorial Hopf algebra
Abstract
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.
Rights Information
Copyright © 2012 Elsevier Inc. All rights reserved.
Terms of Use & License Information
DOI
10.1016/j.aim.2011.12.024
Recommended Citation
Marcelo Aguiar, Carlos André, Carolina Benedetti, Nantel Bergeron, 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, Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras, Advances in Mathematics, Volume 229, Issue 4, 1 March 2012, Pages 2310-2337, ISSN 0001-8708, 10.1016/j.aim.2011.12.024. (http://www.sciencedirect.com/science/article/pii/S0001870812000035)
