Combinatorial Hopf algebra of supercharacters of type D

Abstract

We provide a Hopf algebra structure on the supercharacter theory for the unipotent upper triangular group of type {D} over a finite field. Also, we make further comments with respect to types {B} and {C}. Type {A} was explored by M. Aguiar et. al (2010), thus this extended abstract is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.

Keywords

• hopf algebras
• set partitions of type d
• supercharacters
• unipotent upper triangular groups.
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]