sl2 and its finite-dimensional modules, its weight modules and tools from classical representation theory

(Coxeter=Weyl: ‘Indecomposable projective functors on O 0 .’) Symmetric group: the 2-simples are categorifications of the simples..

The quantized version sheds new light on HOMFLY-PT, Kauffman and Reshetikhin-Turaev polynomials: their symmetries can be explained representation theoretical.. Some parts even work

Daniel Tubbenhauer Colored Jones and HOMFLY-PT polynomials October 2015 26 / 28.. I do not

Daniel Tubbenhauer The virtual Khovanov homology July 2013 11 / 29.+. the complex is an invariant up to chain

Theorem 3.11 implies that if V is a finite dimensional representation of a finite group G, then the complex conjugate representation V (i.e., the same space V with the same addition

The author conjectures that the whole construction can be used as a “blueprint” for a cate- gorification of the virtual sl 3 polynomial (as explained in Section 1.3), since

The six main fields of pure mathematics algebra , analysis , geometry , topology , logic , discrete mathematics?.

•...in the context of the representation theory of Hopf algebras? Fusion rules i.e. tensor products rules... •...in the context of categories? Morphisms of representations and