Tange, R orcid.org/0000-0003-0867-1573 (2023) A Combinatorial Translation Principle and Diagram Combinatorics for the General Linear Group. Transformation Groups, 28 (4). pp. 1687-1719. ISSN 1083-4362
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.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | © 2022, The Author(s). This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Nov 2021 14:02 |
Last Modified: | 29 Oct 2024 14:04 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00031-022-09710-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:180804 |