Geodesic
Kategorie 𝒪, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe
Journal of the American Mathematical Society, Tome 03 (1990) no. 2, pp. 421-445

Voir la notice de l'article provenant de la source American Mathematical Society

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. 
Soergel, Wolfgang. Kategorie 𝒪, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe. Journal of the American Mathematical Society, Tome 03 (1990) no. 2, pp. 421-445. doi: 10.1090/S0894-0347-1990-1029692-5
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