Aguiar, Marcelo and Venkateswaran, Vidya (2012) Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras. Advances in Mathematics, 229 (4). pp. 2310-2337. ISSN 0001-8708 http://resolver.caltech.edu/CaltechAUTHORS:20120314-070105336
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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.
| Item Type: | Article | ||||||||||||||||||||||||
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| Additional Information: | © 2012 Elsevier Inc. Received 6 October 2010; accepted 30 December 2011. Available online 20 January 2012. Communicated by Sara C. Billey. This paper developed during a focused research week at the American Institute of Mathematics in May 2010. The main results presented here were proved as a group during that meeting. | ||||||||||||||||||||||||
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| Subject Keywords: | Supercharacters; Unipotent uppertriangular matrices; Symmetric functions in noncommuting variables; Finite fields; Combinatorial Hopf algebra | ||||||||||||||||||||||||
| Record Number: | CaltechAUTHORS:20120314-070105336 | ||||||||||||||||||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20120314-070105336 | ||||||||||||||||||||||||
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| Official 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) | ||||||||||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||||||||
| ID Code: | 29712 | ||||||||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||||||||||||||
| Deposited On: | 14 Mar 2012 15:57 | ||||||||||||||||||||||||
| Last Modified: | 14 Mar 2012 15:57 |
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