Geodesic
Combinatorial Hopf algebra of superclass functions of type $D$.
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 4, pp. 767-783.

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

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type $D$ over a finite field based on a supercharacter theory constructed by André and Neto in J. Algebra 305, 394--429 (2006) and 322 (2009). Also, we make further comments with respect to types $B$ and $C$. Type $A$ was explored by M. Aguiar et al. in Adv. Math. 229 (2012); thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.
Classification : 16T30, 05E10, 20G05, 20G40
Keywords: supercharacters, set partitions of type $D$, Hopf algebras, unipotent upper triangular matrix groups 
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     author = {Benedetti, Carolina},
     title = {Combinatorial {Hopf} algebra of superclass functions of type $D$.},
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Benedetti, Carolina. Combinatorial Hopf algebra of superclass functions of type $D$.. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 4, pp. 767-783. http://geodesic.mathdoc.fr/item/JAC_2013__38_4_a11/