Emmy-Noether-Seminar: Modular BGG category O and periodic Kazhdan-Lusztig polynomials

Modular BGG category O and periodic Kazhdan-Lusztig polynomials

Quan Situ (Clermont-Ferrand)

Abstract: We consider a modular analogue of BGG category O. It is the category of strongly B-equivariant g-modules, where g is the Lie algebra of a reductive group G over positive characteristic and B is a Borel subgroup of G. Its principal block is a highest weight category, whose underlying poset is the affine Weyl group equipped with the semi-infinite order. We show that the dimension of extension group between simple objects and costandard objects is given by the coefficient of periodic Kazhdan-Lusztig polynomials, when the characteristic is large enough. We will also discuss a connection to the geometry of semi-infinite orbits on the affine flag variety. This is based on a joint work with Simon Riche.