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Restricting Rational Modules to Frobenius Kernels
- Publication Year :
- 2024
-
Abstract
- Let $G$ be a connected reductive group over an algebraically closed field of characteristic $p>0$. Given an indecomposable G-module $M$, one can ask when it remains indecomposable upon restriction to the Frobenius kernel $G_r$, and when its $G_r$-socle is simple (the latter being a strictly stronger condition than the former). In this paper, we investigate these questions for $G$ having an irreducible root system of type A. Using Schur functors and inverse Schur functors as our primary tools, we develop new methods of attacking these problems, and in the process obtain new results about classes of Weyl modules, induced modules, and tilting modules that remain indecomposable over $G_r$.
- Subjects :
- Mathematics - Representation Theory
Mathematics - Group Theory
20G05, 20J06
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.03973
- Document Type :
- Working Paper