This unique book provides the first introduction to crystal base theory from the combinatorial
point of view. Crystal base theory was developed by Kashiwara and Lusztig from the …

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 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 …

Koenig and Xi introduced affine cellular algebras. Kleshchev and Loubert (and Miemietz)
showed that an important class of infinite-dimensional algebras, the Khovanov–Lauda …

Laurent phenomenon and simple modules of quiver Hecke algebras Page 1 Laurent phenomenon
and simple modules of quiver Hecke algebras Masaki Kashiwara and Myungho Kim Compositio …

This paper develops a general theory of canonical bases and how they arise naturally in the
context of categorification. As an application, we show that Lusztig's canonical basis in the …

In this paper, we study 2-representations of 2-quantum groups (in the sense of Rouquier and
Khovanov-Lauda) categorifying tensor products of irreducible representations. Our aim is to …

We construct a monoidal category C w, v which categorifies the doubly-invariant algebra
CN′(w)[N] N (v) associated with Weyl group elements w and v. It gives, after a localization …

Representations of Khovanov–Lauda–Rouquier algebras III: symmetric affine type |
SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find a journal …

We define and study RoCK blocks for double covers of symmetric groups. We prove that
RoCK blocks of double covers are Morita equivalent to standardlocal'blocks. The analogous …