n-Cohomology of simple highest weight modules on walls and purity

  title={n-Cohomology of simple highest weight modules on walls and purity},
  author={Wolfgang Soergel},
  journal={Inventiones mathematicae},
  • W. Soergel
  • Published 1 October 1989
  • Mathematics
  • Inventiones mathematicae
SummaryLetG⊃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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