Combinatorial Hopf algebras from representations of families of wreath products

Abstract

We construct Hopf algebras whose elements are representations of combinatorial automorphism groups, by generalising a theorem of Zelevinsky on Hopf algebras of representations of wreath products. As an application we attach symmetric functions to representations of graph automorphism groups, generalising and refining Stanley's chromatic symmetric function.

arXiv comment29 pages. v3: minor edits