Antipode and Primitive elements in the Hopf Monoid of Super Characters
Journal Article
Overview
abstract
From a recent paper, we recall the Hopf monoid structure on the; supercharacters of the unipotent uppertriangular groups over a finite field. We; give cancelation free formula for the antipode applied to the bases of class; functions and power sum functions, giving new cancelation free formulae for the; standard Hopf algebra of supercharacters and symmetric functions in; noncommuting variables. We also give partial results for the antipode on the; supercharacter basis, and explicitly describe the primitives of this Hopf; monoid.
