Twisting functors on 𝒪

Andersen, Henning; Stroppel, Catharina

doi:10.1090/S1088-4165-03-00189-4

Twisting functors on $\mathcal {O}$
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by Henning Haahr Andersen and Catharina Stroppel

Represent. Theory 7 (2003), 681-699

DOI: https://doi.org/10.1090/S1088-4165-03-00189-4

Published electronically: December 3, 2003

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Abstract:

This paper studies twisting functors on the main block of the Bernstein-Gelfand-Gelfand category $\mathcal {O}$ and describes what happens to (dual) Verma modules. We consider properties of the right adjoint functors and show that they induce an auto-equivalence of derived categories. This allows us to give a very precise description of twisted simple objects. We explain how these results give a reformulation of the Kazhdan-Lusztig conjectures in terms of twisting functors.

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