Quantum Frobenius Heisenberg categorification

Abstract

We associate a diagrammatic monoidal category $\mathcal{H}{\text{eis}}_k(A;z,t)$, which we call the quantum Frobenius Heisenberg category, to a symmetric Frobenius superalgebra $A$, a central charge $k\in \mathbb{Z}$, and invertible parameters $z,t$ in some ground ring. When $A$ is trivial, i.e. it equals the ground ring, these categories recover the quantum Heisenberg categories introduced in our previous work, and when the central charge $k$ is zero they yield generalizations of the affine HOMFLY-PT skein category. By exploiting some natural categorical actions of $\mathcal{H}{\text{eis}}_k(A;z,t)$ on generalized cyclotomic quotients, we prove a basis theorem for morphism spaces.

arXiv comment44 pages

References in corpus (10)

• Monoidal supercategories
• Hecke algebras, finite general linear groups, and Heisenberg categorification
• A general approach to Heisenberg categorification via wreath product algebras
• On the definition of quantum Heisenberg category
• Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
• Frobenius Heisenberg categorification
• Affine wreath product algebras
• The Elliptic Hall algebra and the deformed Khovanov Heisenberg category
• Foundations of Frobenius Heisenberg categories
• W-algebras from Heisenberg categories

Cited by in corpus (7)

• On the definition of quantum Heisenberg category
• Frobenius Heisenberg categorification
• Unfurling Khovanov-Lauda-Rouquier algebras
• Affinization of monoidal categories
• The quantum isomeric supercategory
• String diagrams and categorification
• Affine oriented Frobenius Brauer categories