Caratterizzazione dei gruppi immagini omomorfe duali di un gruppo finito
Nous catégorifions explicitement les coefficients de la matrice de la représentation de Burau en utilisant des méthodes géométriques élémentaires. Nous montrons que cette catégorification est fidèle dans le sens où elle détecte la tresse triviale.
We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
In this paper we study the BGG-categories associated to quantum groups. We prove that many properties of the ordinary BGG-category for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for and for finite dimensional -modules we are able to determine...