Integration of Modules I: Stability
Representation Theory
2019-10-30 v6 Group Theory
Rings and Algebras
Abstract
We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for passing from stability to an algebraic group action. As an application, we prove integrability of bricks for a semisimple algebraic group.
Cite
@article{arxiv.1708.06620,
title = {Integration of Modules I: Stability},
author = {Dmitriy Rumynin and Matthew Westaway},
journal= {arXiv preprint arXiv:1708.06620},
year = {2019}
}
Comments
Version 2: Some changes in terminology, examples of over-restricted modules are added. Version 3: mistakes in tables are corrected. Version 4: major revision, the paper is split into two parts, the exponential part is published separately (see arXiv:1807.08698). Version 5: minor corrections. Version 6: final, minor corrections