A combinatorial translation principle and diagram combinatorics for the general linear group
Abstract
Let k be an algebraically closed field of characteristic p>0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and the decomposition numbers for the general linear group over k in terms of cap diagrams under the assumption that p is bigger than the greatest hook length in the partitions involved. Then we introduce and study the rational Schur functor from a category of GL_n-modules to the category of modules for the walled Brauer algebra. As a corollary we obtain the decomposition numbers for the walled Brauer algebra when p is bigger than the greatest hook length in the partitions involved. This is a sequel to an earlier paper on the symplectic group and the Brauer algebra.
Cite
@article{arxiv.2011.05564,
title = {A combinatorial translation principle and diagram combinatorics for the general linear group},
author = {Rudolf Tange},
journal= {arXiv preprint arXiv:2011.05564},
year = {2023}
}
Comments
This paper is a continuation of arXiv:2011.03606 and arXiv:0806.4500, and it shares some general notation with both. To appear in Transformation Groups