Seminar by Daniel Tubbenhauer (Mathematisches Institut, Göttingen)

Title: sl3-WEB BASES AND CATEGORIFICATION

2013.09.10 | Christine Dilling

Date Wed 02 Oct
Time 15:15 16:15
Location Aud. D3

Abstract
The representation categories Rep(Uq(sln))of the quantumgroups Uq(sln) are knownto have a graphical and combinatorial presentation, the so-called sln-web categories orsln-spiders.These categories have connections to the sln-link polynomials and various aspects of combinatorics.After Khovanov published his groundbreaking work on the arc algebra Hn, that can be seen asa categorification of the sl2-web category, researchers started to introduce other graphical categorificationsof 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 thesl3-web category, that we callsl3-web algebra, contain the various bases of the sl3-web space WS in a natural way.

Seminar