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Representation Theory

ISSN 1088-4165



Twisting functors on $\mathcal {O}$

Authors: Henning Haahr Andersen and Catharina Stroppel
Journal: Represent. Theory 7 (2003), 681-699
MSC (2000): Primary 17B10, 17B35, 20F29
Published electronically: December 3, 2003
MathSciNet review: 2032059
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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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Additional Information

Henning Haahr Andersen
Affiliation: Department of Mathematics, University of Aarhus, Dk-8000 Aarhus C, Denmark

Catharina Stroppel
Affiliation: Department of Mathematics and Computer Science, Leicester University, GB Leicester LE1 7RH
Address at time of publication: University of Aarhus, Ny Munkegade 530, Dk-8000 Aarhus C, Denmark

Received by editor(s): February 27, 2003
Received by editor(s) in revised form: July 10, 2003
Published electronically: December 3, 2003
Article copyright: © Copyright 2003 by the authors