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

Peter Fiebig, Geordie Williamson (2014)

Annales de l’institut Fourier

We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. 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 a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.

The F-method and a branching problem for generalized Verma modules associated to ( Lie G 2 , so ( 7 ) )

Todor Milev, Petr Somberg (2013)

Archivum Mathematicum

The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras Lie G 2 i so ( 7 ) , and generalized conformal so ( 7 ) -Verma modules of scalar type. As a result, we classify the i ( Lie G 2 ) 𝔭 -singular vectors for this class of so ( 7 ) -modules.

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