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. © 2011 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.
CITATION STYLE
Aguiar, M., André, C., Benedetti, C., Bergeron, N., Chen, Z., Diaconis, P., … Zabrocki, M. (2011). Supercharacters, symmetric functions in noncommuting variables, extended abstract. In FPSAC’11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics (pp. 3–14). https://doi.org/10.46298/dmtcs.2967
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