A remarkable functor on $G$-modules
Representation Theory
2026-04-28 v3
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.
Cite
@article{arxiv.2505.07144,
title = {A remarkable functor on $G$-modules},
author = {Joe Baine and Tasman Fell and Anna Romanov and Alexander Sherman and Geordie Williamson},
journal= {arXiv preprint arXiv:2505.07144},
year = {2026}
}
Comments
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