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arXiv · 1703.02457

The center of the small quantum group II: singular blocks

Anna Lachowska·You Qi
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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.

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BibTeXRIS

Anna Lachowska, You Qi. 2017-03-07. The center of the small quantum group II: singular blocks. https://doi.org/10.1112/plms.12193

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