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Supercharacters, symmetric functions in noncommuting variables (extended abstract)

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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Marcelo Aguiar, Carlos André, Carolina Benedetti, Nantel Bergeron, Zhi Chen, et al.. Supercharacters, symmetric functions in noncommuting variables (extended abstract). 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.3-14, ⟨10.46298/dmtcs.2967⟩. ⟨hal-01336771⟩



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