The center of the small quantum group 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.

36 pages, 3 figures, comments welcome. Minor corrections and updated references

Cited by in corpus (5)

• Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants
• The center of small quantum groups I: the principal block in type A
• Remarks on the derived center of small quantum groups
• A computer algorithm for the BGG resolution
• On certain Hochschild cohomology groups for the small quantum group