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

By Marcelo Aguiar, C. André, C. Benedetti, Nantel Bergeron, Zhi Chen, Persi Diaconis, Anders O. F. Hendrickson, Samuel K. Hsiao, I. Isaacs, A. Jedwab and 18 more. 2010

95 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/170d1f5d7c95a3b7320184a2ba088aceb21597bc

Citations in the corpus

• Hopf Algebras in Combinatorics (2014, unknown): “where [n]!q := [n]q[n− 1]q · · · [2]q[1]q and [n]q := 1 + q + · · ·+ qn−1 = q −1 q−1 .”