English

Differential operators on quantized flag manifolds at roots of unity II

Representation Theory 2015-01-14 v2

Abstract

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 DD-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.

Keywords

Cite

@article{arxiv.1101.5848,
  title  = {Differential operators on quantized flag manifolds at roots of unity II},
  author = {Toshiyuki Tanisaki},
  journal= {arXiv preprint arXiv:1101.5848},
  year   = {2015}
}

Comments

42 pages, final version to appear in Nagoya Mathematical Journal. arXiv admin note: text overlap with arXiv:1002.0113