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 GLn-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.
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TANGE, R. A COMBINATORIAL TRANSLATION PRINCIPLE AND DIAGRAM COMBINATORICS FOR THE GENERAL LINEAR GROUP. Transformation Groups 28, 1687–1719 (2023). https://doi.org/10.1007/s00031-022-09710-2
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DOI: https://doi.org/10.1007/s00031-022-09710-2