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

By P. Fiebig, Geordie Williamson. 2010

52 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9f68ad425bf46636b62f119550a135a81a1d9c0e

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In Discrete Mathematics and Combinatorics

1. Geordie Williamson
2. Ben Elias
3. Simon Riche

In Geometry and Topology

1. Geordie Williamson
2. Ben Elias
3. Simon Riche

In Mathematical Physics

1. Geordie Williamson
2. Ben Elias

Citations in the corpus

• Schubert calculus and torsion explosion (2013, methodology): “t around the Steinberg weight.5 This algorithm (in a slightly different form) was discovered independently by Libedinsky [Lib]. 3One can also perform this calculation using the theory of moment graphs [FW]. However the computations using generators and relations are generally much simpler. 4The termi”