Derived Functors Related to Wall-Crossing

Abstract

The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this transformation is a left exact functor. This functor and its first derived functor are evaluated on the global sections of a line bundle on the flag variety. It is conjectured that the derived functors of order greater than one annihilate the global sections. Also, the principal indecomposable modules for the Frobenius subgroups are shown to be acyclic.

Key Words:

• Derived functors
• Linear algebraic groups

2000 Mathematics Subject Classification:

• 20G05

Notes

Communicated by D. Nakano.