Room P4.35, Mathematics Building
Marco Mackaay, Univ. Algarve
web algebras, cyclotomic KLR algebras and categorical quantum skew Howe duality
I will introduce web algebras , which involve Kuperberg's web space and Khovanov foams with boundary in . These algebras are the analogues of Khovanov's arc algebras. I will show how the 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 is isomorphic to and that, under this isomorphism, the indecomposable projective -modules, which Robert constructs explicitly, correspond precisely to the dual canonical basis elements in .