Categorification of quantum boson algebras
Quantum Algebra
2025-09-16 v1 Representation Theory
Abstract
We produce graded monoidal categorifications of the quantum boson algebras in any symmetrizable Kac-Moody type. Our categories are defined in terms of diagrammatic generators and relations and have a faithful 2-representation on Khovanov-Lauda and Rouquier's categorification of the corresponding positive part quantum group. We use our construction to produce interesting bases of the quantum boson algebras and quantum bosonic extensions.
Cite
@article{arxiv.2509.12163,
title = {Categorification of quantum boson algebras},
author = {Sam Qunell},
journal= {arXiv preprint arXiv:2509.12163},
year = {2025}
}
Comments
38 pages. Several tikz figures