Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties

Details Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties

2010-08-04

arxiv.org/abs/1008.0719v2

Mathematics

Representation Theory

47 pages, minor revision

Scientific paper

We show that, with coefficients in a field or a complete local ring k, the Braden-MacPherson algorithm computes the stalks of parity sheaves with coefficients in k. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the p-smooth locus of (Kac-Moody) Schubert varieties agrees with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.

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