The center of the small quantum group II: singular blocks
Abstract
We generalize to the case of singular blocks the result in 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 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 lth root of unity is formulated in type A.
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