, Volume 98, Issue 3, pp 565-580

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

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Summary

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.

Written during the author's stay at MSRI, supported by a Stipendium der Clemens-Plassmann-Stiftung