A Quantum McKay Correspondence

Abstract: 

The classical McKay correspondence characterises finite subgroups of SU(2) by associating them with a very restrictive family of graphs.  

This can be rephrased in modern language as a classification of modulecategories over the category of finite-dimensional representations ofthe Lie algebra sl2.  Through this perspective, we will introduce a"quantum" version of the McKay correspondence for SU(2) and describe howcurrent research is attempting to generalise these results.