A \(\mathrm{GL}(\mathbb{F}_q)\)-compatible Hopf algebra of unitriangular class functions

DOI10.1016/j.jalgebra.2023.05.040zbMath1521.20104arXiv2211.05960OpenAlexW4379744340MaRDI QIDQ6114011

Lucas Gagnon

Publication date: 11 July 2023

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.05960

zbMATH Keywords

finite fieldHopf algebrageneral linear groupclass functionHopf monoidunipotent groupinduction functor

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Representation theory for linear algebraic groups (20G05) Hopf algebras and their applications (16T05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chromatic quasisymmetric functions
• Hopf monoids from class functions on unitriangular matrices
• A supercharacter analogue for normality.
• Super-characters of finite unipotent groups of types \(B_n\), \(C_n\) and \(D_n\).
• The Hopf monoid on nonnesting supercharacters of pattern groups
• Representations of finite classical groups. A Hopf algebra approach
• An application of Hopf-algebra techniques to representations of finite classical groups
• Basic characters of the unitriangular group
• Combinatorial Hopf algebra of superclass functions of type \(D\).
• Monoidal Functors, Species and Hopf Algebras
• Hopf monoids in the category of species
• Characters of Reductive Groups over a Finite Field. (AM-107)
• A combinatorial formula for Macdonald polynomials
• Supercharacters and superclasses for algebra groups
• Pattern groups and a poset based Hopf monoid

This page was built for publication: A \(\mathrm{GL}(\mathbb{F}_q)\)-compatible Hopf algebra of unitriangular class functions