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Kategorie O, Perverse Garben Und Moduln Uber Den Koinvariantez Zur Weylgruppe

Wolfgang Soergel
Journal of the American Mathematical Society
Vol. 3, No. 2 (Apr., 1990), pp. 421-445
DOI: 10.2307/1990960
Stable URL: http://www.jstor.org/stable/1990960
Page Count: 25
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Kategorie  O, Perverse Garben Und Moduln Uber Den Koinvariantez Zur Weylgruppe
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Abstract

We give a description of "the algebra of category O which is explicit enough to prove that the structure of the direct summands of 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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