The Hopf monoid on nonnesting supercharacters of pattern groups

Abstract

We construct supercharacter theories for a collection of unipotent matrix groups and produce a Hopf monoid from the supercharacters. These supercharacter theories are coarser than those defined by Diaconis--Isaacs for algebra groups and have supercharacters and superclasses indexed by nonnesting labeled set partitions. We compute the supercharacter tables and describe the product and coproduct of the Hopf monoid combinatorially. We also show that this Hopf monoid is free.

Final version; DOI added

References in corpus (1)

• Representations of Finite Unipotent Linear Groups by the Method of Clusters

Cited by in corpus (2)

• Hopf Algebras and Markov Chains
• Supercharacter theories of dihedral groups