We construct knot invariants categorifying the quantum knot variants for all representations
of quantum groups. We show that these invariants coincide with previous invariants defined …

We prove that the quantum cluster algebra structure of a unipotent quantum coordinate ring
$ A_q (\mathfrak {n}(w)) $, associated with a symmetric Kac–Moody algebra and its Weyl …

We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting
with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with …

In this paper, we prove Khovanov-Lauda's cyclotomic categorification conjecture for all
symmetrizable Kac-Moody algebras. Let U_q(g) be the quantum group associated with a …

Let J be a set of pairs consisting of good U'_q (\mathfrak g) U q′(g)-modules and invertible
elements in the base field\mathbb C (q) C (q). The distribution of poles of normalized R …

Simplicity of heads and socles of tensor products Page 1 Simplicity of heads and socles of
tensor products Seok-** Kang, Masaki Kashiwara, Myungho Kim and Se-** Oh Compositio …

We give an algebraic construction of standard modules—infinite-dimensional modules
categorifying the Poincaré–Birkhoff–Witt basis of the underlying quantized envelo** …

We classify simple representations of Khovanov–Lauda–Rouquier algebras in finite type.
The classification is in terms of a standard family of representations that is shown to yield the …