Room P4.35, Mathematics Building

Marco Mackaay, Univ. Algarve
𝔰𝔩 3 web algebras, cyclotomic KLR algebras and categorical quantum skew Howe duality

I will introduce 𝔰𝔩 3 web algebras K(S), which involve Kuperberg's 𝔰𝔩 3 web space W(S) and Khovanov 𝔰𝔩 3 foams with boundary in W(S). These algebras are the 𝔰𝔩 3 analogues of Khovanov's 𝔰𝔩 2 arc algebras. I will show how the K(S) 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(S) is isomorphic to W(S) and that, under this isomorphism, the indecomposable projective K(S)-modules, which Robert constructs explicitly, correspond precisely to the dual canonical basis elements in W(S).
Categorification mini-workshop