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arXiv · 2505.07144

A remarkable functor on $G$-modules

Joe Baine·Tasman Fell·Anna Romanov·Alexander Sherman·Geordie Williamson
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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.

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Joe Baine, Tasman Fell, Anna Romanov, Alexander Sherman, Geordie Williamson. 2025-05-11. A remarkable functor on $G$-modules. https://arxiv.org/abs/2505.07144

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