Proceedings of The London Mathematical Society | 2019
The center of small quantum groups II: singular blocks
Abstract
We generalize to the case of singular blocks the result in \\cite{BeLa} that describes the center of the principal block of a small quantum group in terms of sheaf cohomology over the Springer resolution. Then using the method developed in \\cite{LQ1}, we present a linear algebro-geometric approach to compute the dimensions of the singular blocks and of the entire center of the small quantum group associated with a complex semisimple Lie algebra. A conjectural formula for the dimension of the center of the small quantum group at an $l$th root of unity is formulated in type A.