A remarkable functor on $G$-modules

Abstract

We introduce a new functor on categories of modular representations of reductive algebraic groups. Our functor has remarkable properties. For example it is a tensor functor and sends every standard and costandard object in the principal block to a one-dimensional object. We connect our functor to recent work of Gruber and conjecture that our functor is equivalent to hypercohomology under the equivalence of the Finkelberg-Mirkovic conjecture.

Improved understanding of grading on functor for different blocks in Section 4. Improved exposition, fixed further typos and updated references. Nearly identitical to published version to appear