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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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Wall-crossing functors and $\mathcal {D}$-modules
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by Alexander Beilinson and Victor Ginzburg PDF
Represent. Theory 3 (1999), 1-31 Request permission


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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Additional 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