Modular perverse sheaves on flag varieties I: tilting and parity sheaves

Pramod N. Achar (1) , Simon Riche (2, 3)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group is a "graded version" of the category of tilting perverse sheaves on the flag variety of the dual group, for any field of coefficients whose characteristic is good. We derive some consequences on Soergel's modular category O, and on multiplicities and decomposition numbers in the category of perverse sheaves.

Domaines: Théorie des représentations [math.RT]; Mathématiques [math]

Pramod N. Achar, Simon Riche. Modular perverse sheaves on flag varieties I: tilting and parity sheaves. Annales Scientifiques de l'École Normale Supérieure, 2016, 49, pp.325-370. ⟨hal-00937989v2⟩