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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Twisting functors on $\mathcal {O}$
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by Henning Haahr Andersen and Catharina Stroppel PDF
Represent. Theory 7 (2003), 681-699

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.
References
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Additional Information
  • Henning Haahr Andersen
  • Affiliation: Department of Mathematics, University of Aarhus, Dk-8000 Aarhus C, Denmark
  • Email: mathha@imf.au.dk
  • 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
  • Email: cs93@le.ac.uk, stroppel@imf.au.dk
  • Received by editor(s): February 27, 2003
  • Received by editor(s) in revised form: July 10, 2003
  • Published electronically: December 3, 2003
  • © Copyright 2003 by the authors
  • Journal: Represent. Theory 7 (2003), 681-699
  • MSC (2000): Primary 17B10, 17B35, 20F29
  • DOI: https://doi.org/10.1090/S1088-4165-03-00189-4
  • MathSciNet review: 2032059