Published March 1, 2012
| public
Journal Article
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
- Creators
- Aguiar, Marcelo
- Venkateswaran, Vidya
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.
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.Additional details
- Eprint ID
- 29712
- DOI
- 10.1016/j.aim.2011.12.024
- Resolver ID
- CaltechAUTHORS:20120314-070105336
- DMS-1001935
- NSF
- NSERC
- DMS-0804324
- NSF
- DMS 07-01291
- NSF
- H98230-10-1-0362
- NSA
- DMS-0854893
- NSF
- DMS-0652641
- NSF
- NDSEG Fellowship
- CRC
- DMS-0854849
- NSF
- Beca Mazda
- Created
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2012-03-14Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field