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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Kategorie $\mathcal {O}$, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe
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by Wolfgang Soergel PDF
J. Amer. Math. Soc. 3 (1990), 421-445 Request permission


We give a description of “the algebra of category $\mathcal {O}$” which is explicit enough to prove that the structure of the direct summands of $\mathcal {O}$ depends only on the integral Weyl group and the singularity of the central character, as well as to establish a weak version of the duality conjectures of Beilinson and Ginsburg [BGi]. As a byproduct we describe the intersection cohomology of Schubert varieties as modules over global cohomology ring. These are certain indecomposable graded self-dual modules over the coinvariant algebra of the Weyl group, via the Borel picture for the global cohomology ring of a flag manifold. They play a central role in this article and should have an interesting future.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 3 (1990), 421-445
  • MSC: Primary 17B35
  • DOI:
  • MathSciNet review: 1029692