Summary
LetG⊃P⊃B be respectively a complex connected linear algebraic semisimple group, a parabolic subgroup and a Borel subgroup. The first main result is the following theorem: Let ℱ be a pure complex onG/B, smooth with respect to Bruhat cells. Then its restriction to anyP-orbit is pure as well, of the same weight. As a consequence we are able to compute then-cohomology of simple highest weight modules on walls.
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Written during the author's stay at MSRI, supported by a Stipendium der Clemens-Plassmann-Stiftung
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Soergel, W. n-Cohomology of simple highest weight modules on walls and purity. Invent Math 98, 565–580 (1989). https://doi.org/10.1007/BF01393837
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DOI: https://doi.org/10.1007/BF01393837