Singular Rouquier complexes

Rouquier Complexes

1.1. Setup. In this talk k is a field of characteristic 0. Let (W,S) be a Coxeter group with |S| = n < ∞. Also we let V = ∑ s∈S kes be the reflection representation of W , and R = k[V ]. R is a graded algebra with V ∗ in degree 2. We abbreviate M ⊗R N = MN for a right R-module M and a left R-module N . We let {αs}s∈S be the dual basis of {es}s∈S , which can be considered as elements in V ∗ ⊂ R....

Rouquier Complexes are Functorial over Braid Cobordisms

Using the diagrammatic calculus for Soergel bimodules developed by B. Elias and M. Khovanov, we show that Rouquier complexes are functorial over braid cobordisms. We explicitly describe the chain maps which correspond to movie move generators.

Beyond Rouquier Partitions

We obtain closed formulas, in terms of Littlewood-Richardson coefficients, for the canonical basis elements of the Fock space representation of Uv(ŝle) which are labelled by partitions having ‘locally small’ e-quotients and arbitrary e-cores. We further show that upon evaluation at v = 1, this gives the corresponding decomposition numbers of the q-Schur algebra in characteristic l (where q is a...

Semi-Simplicial Complexes and Singular Homology

Representations of Khovanov-lauda-rouquier Algebras Iii: Symmetric Affine Type

We develop the homological theory of KLR algebras of symmetric affine type. For each PBW basis, a family of standard modules is constructed which categorifies the PBW basis.