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

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

2010-09-21

arxiv.org/abs/1009.4134v2

Advances in Mathematics 229 (2012) 2310--2337

Mathematics

Combinatorics

To Appear in Advances in Mathematics (2012), 23 pages

Scientific paper

10.1016/j.aim.2011.12.024

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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