This expository article explains how planar diagrammatics naturally arise in the study of
categorified quantum groups with a focus on the categorification of quantum sl2. We derive …

Given a finite subgroup Γ⊂ SL 2 (C) we define an additive 2-category H Γ whose
Grothendieck group is isomorphic to an integral form h Γ of the Heisenberg algebra. We …

We develop a graded version of the theory of cyclotomic q-Schur algebras, in the spirit of the
work of Brundan-Kleshchev on Hecke algebras and of Ariki on q-Schur algebras. As an …

We associate a monoidal category H _B HB, defined in terms of planar diagrams, to any
graded Frobenius superalgebra B. This category acts naturally on modules over the wreath …

We show that any Abelian module category over the (degenerate or quantum) Heisenberg
category satisfying suitable finiteness conditions may be viewed as a 2-representation over …

We revisit the definition of the Heisenberg category of central charge k∈ Z. For central
charge− 1, this category was introduced originally by Khovanov, but with some additional …

We introduce a diagrammatic monoidal category ℋ eisk (z, t) which we call the quantum
Heisenberg category; here, k∈ ℤ is “central charge” and z and t are invertible parameters …

We associate a graded monoidal supercategory HeisF, k to every graded Frobenius
superalgebra F and integer k. These categories, which categorify a broad range of lattice …

We associate a monoidal category H λ to each dominant integral weight λ of sl ˆ p or sl∞.
These categories, defined in terms of planar diagrams, act naturally on categories of …

In this paper, we construct a categorical double quantum Heisenberg action on the
representation category of finite classical groups $\mathrm {O} _ {2n+ 1}(q) $, $\mathrm {Sp} …