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Published March 1, 2012 | public
Journal Article

Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

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

Created:
August 22, 2023
Modified:
October 24, 2023