Differential operators on quantized flag manifolds at roots of unity II

Details Differential operators on quantized flag manifolds at roots of unity II Differential operators on quantized flag manifolds at roots of unity II

2011-01-31

arxiv.org/abs/1101.5848v1

Mathematics

Representation Theory

41 pages

Scientific paper

We formulate a Beilinson-Bernstein type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping algebra at a root of 1 with fixed regular Harish-Chandra central character and the category of certain twisted $D$-modules on the corresponding quantized flag manifold. We show that the proof is reduced to a statement about the (derived) global sections of the ring of differential operators on the quantized flag manifold. We also give a reformulation of the conjecture in terms of the (derived) induction functor.

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