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.

44 pages

References in corpus (2)

• On the definition of quantum Heisenberg category
• Foundations of Frobenius Heisenberg categories

Cited by in corpus (4)

• On the definition of quantum Heisenberg category
• Affinization of monoidal categories
• The quantum isomeric supercategory
• Affine oriented Frobenius Brauer categories