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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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Wall-crossing functors and $\mathcal {D}$-modules
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by Alexander Beilinson and Victor Ginzburg
Represent. Theory 3 (1999), 1-31
Published electronically: January 11, 1999


We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using ${\mathcal {D}}$-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the Structure-theorem; two important results were established earlier by W. Soergel in a totally different way. Other applications to the category ${\mathcal {O}}$ of Bernstein-Gelfand-Gelfand are given, and some conjectural relationships between Koszul duality, Verdier duality and convolution functors are discussed. A geometric interpretation of tilting modules is given.
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Bibliographic Information
  • Alexander Beilinson
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • MR Author ID: 33735
  • Email:
  • Victor Ginzburg
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • Email:
  • Published electronically: January 11, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 1-31
  • MSC (1991): Primary 05E99, 17B37
  • DOI:
  • MathSciNet review: 1659527