Derived Functors Related to Wall Crossing

Details Derived Functors Related to Wall Crossing Derived Functors Related to Wall Crossing

2008-02-29

arxiv.org/abs/0803.0008v2

Mathematics

Representation Theory

14 pages, revised and expanded, accepted by Communications in Algebra

Scientific paper

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.

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