Cellular algebras an tilting modules for quantum sl2

Title: Cellular algebras an tilting modules for quantum sl2

 

Speaker G. Lehrer Prof. , University of Sydney

 

Time1000-1100am; June 6; 2013

 

PlaceConference Room A404, Department of Mathematical Sciences

 

AbstractLet _e A(d) be the simple module with highest weight d of Ue A, an integral form of quantum sl2, where e A is a suitable localisation of the ring A = Z[q_12 ]. We exhibit for all positive integers r an explicit cellular structure for EndU eA(_ e A(d)r), through a description of this endomorphism algebra by dia-grams. When _ is a root of unity of order bigger than d we consider the spe-cialisation __(d)r at q 7! _ of _e A(d)r. Using some general results concerning representations, we connect the decompositions numbers of EndU_(__(d)r) with the weights of the tilting modules for quantum sl2 at q = _. This is joint work with Henning Andersen and Ruibin Zhang.

 

ContactHechun Zhang