Aarhus University Seal / Aarhus Universitets segl

sl3-WEB BASES AND CATEGORIFICATION

Daniel Tubbenhauer
(Mathematisches Institut, Göttingen)
Seminar
Wednesday, 2 October, 2013, at 15:15-16:15, in Aud. D3 (1531-215)
Abstract:
The representation categoriesRep(Uq(sln)) of the quantumgroups Uq(sln) are known
to have a graphical and combinatorial presentation, the so-called sln-web categories or sln-spiders.
These categories have connections to the sln-link polynomials and varies aspects of combinatorics.
After Khovanov published his groundbreaking work on the arc algebra Hn, that can be seen as
a categorification of the sl2-web category, researchers started to introduce other graphical categorifications
of web categories. These are known to have connections to higher link homologies, e.g.
Khovanov homologies, to q-representation theory via higher skew Howe duality, e.g. category O,
KLR and varies Hecke algebras, combinatorial algebraic geometry, e.g. Springer fibers, etc.
I discuss how modules of our (joint work with Marco Mackaay and Weiwei Pan) graphical categorification
of the sl3-web category, that we call sl3-web algebra, contain the varies bases of the
sl3-web space WS in a natural way.
Organised by: QGM
Contact person: Jørgen Ellegaard Andersen