Supercharacters, Symmetric Functions in Noncommuting Variables, and Related Hopf Algebras

Document Type



Mathematics (Pomona)

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supercharacters, unipotent uppertriangular matrices, symmetric functions in noncommuting variables, finite fields, combinatorial Hopf algebra


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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