Geodesic
The antipode and primitive elements in the Hopf monoid of supercharacters
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 903-938.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

From a recent paper, we recall the Hopf monoid structure on the supercharacters of the unipotent uppertriangular groups over a finite field. We give cancellation-free formula for the antipode applied to the bases of class functions and power sum functions, giving new cancellation-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.
Classification : 05E05, 16T05, 20C15
Keywords: antipode, Hopf monoid, supercharacters, primitive elements, symmetric functions in noncommuting variables 
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     title = {The antipode and primitive elements in the {Hopf} monoid of supercharacters},
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Baker-Jarvis, Duff; Bergeron, Nantel; Thiem, Nathaniel. The antipode and primitive elements in the Hopf monoid of supercharacters. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 4, pp. 903-938. http://geodesic.mathdoc.fr/item/JAC_2014__40_4_a9/