Inventiones mathematicae

, Volume 98, Issue 3, pp 565–580

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


  • W. Soergel
    • Max-Planck-Institut für Mathematik

DOI: 10.1007/BF01393837

Cite this article as:
Soergel, W. Invent Math (1989) 98: 565. doi:10.1007/BF01393837


LetGPB 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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© Springer-Verlag 1989