Title

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.

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Copyright © 2012 Elsevier Inc. All rights reserved.

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