The MathNet Korea
Information Center for Mathematical Science

PAC

Information Center for Mathematical Science

PAC

Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
Author Persi Diaconis (Stanford University)
Homepage Url http://www-stat.stanford.edu/~cgates/PERSI/year.html
Coauthors Marcelo Aguiar, Carlos Andr´e, Carolina Benedetti, Nantel Bergeron, Zhi Chen, Anders Hendrickson, Samuel Hsiao, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le, S
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.
Abstract Url http://www-stat.stanford.edu/~cgates/PERSI/papers/superchar-2009.pdf