Kategorie 𝒪, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe

Soergel, Wolfgang

doi:10.1090/S0894-0347-1990-1029692-5

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

Abstract:

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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