# Seminário de Teoria Quântica do Campo Topológica

### ${\mathrm{𝔰𝔩}}_{3}$ web algebras, cyclotomic KLR algebras and categorical quantum skew Howe duality

I will introduce ${\mathrm{𝔰𝔩}}_{3}$ web algebras $K\left(S\right)$, which involve Kuperberg's ${\mathrm{𝔰𝔩}}_{3}$ web space $W\left(S\right)$ and Khovanov ${\mathrm{𝔰𝔩}}_{3}$ foams with boundary in $W\left(S\right)$. These algebras are the ${\mathrm{𝔰𝔩}}_{3}$ analogues of Khovanov's ${\mathrm{𝔰𝔩}}_{2}$ arc algebras. I will show how the $K\left(S\right)$ are related to cyclotomic Khovanov-Lauda-Rouquier algebras (cyclotomic KLR algebras, for short) by a categorification of quantum skew Howe duality. This talk is closely related to the next one by Robert. In particular, I will show that the Grothendieck group of $K\left(S\right)$ is isomorphic to $W\left(S\right)$ and that, under this isomorphism, the indecomposable projective $K\left(S\right)$-modules, which Robert constructs explicitly, correspond precisely to the dual canonical basis elements in $W\left(S\right)$.
Categorification mini-workshop

Organizadores correntes: Roger Picken, Marko Stošić.

Projecto FCT PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry.