Frobenius Heisenberg categorification

Abstract

We associate a graded monoidal supercategory $\mathcal{H}{eis}_{F,k}$ to every graded Frobenius superalgebra $F$ and integer $k$. These categories, which categorify a broad range of lattice Heisenberg algebras, recover many previously defined Heisenberg categories as special cases. In this way, the categories $\mathcal{H}{eis}_{F,k}$ serve as a unifying and generalizing framework for Heisenberg categorification. Even in the case of previously defined Heisenberg categories, we obtain new, more efficient, presentations of these categories, based on an approach of Brundan. When $k=0$, our construction yields new versions of the affine oriented Brauer category depending on a graded Frobenius superalgebra.

29 pages. v2: Minor corrections. v3: Minor corrections and notation change; published version

References in corpus (10)

• Monoidal supercategories
• On the definition of quantum Heisenberg category
• Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
• Representations of the oriented skein category
• Affine wreath product algebras
• The degenerate Heisenberg category and its Grothendieck ring
• Quantum Frobenius Heisenberg categorification
• A basis theorem for the degenerate affine oriented Brauer-Clifford supercategory
• A graphical calculus for the Jack inner product on symmetric functions
• Quantum affine wreath algebras

Cited by in corpus (12)

• On the definition of quantum Heisenberg category
• Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
• Affine wreath product algebras
• Foundations of Frobenius Heisenberg categories
• Quantum Frobenius Heisenberg categorification
• Quantum affine wreath algebras
• String diagrams and categorification
• Group partition categories
• Affine oriented Frobenius Brauer categories
• Diagrammatics for real supergroups
• Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category
• Affine Frobenius Brauer Categories