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Tange, R orcid.org/0000-0003-0867-1573 (2023) Injective and Tilting Resolutions and a Kazhdan-Lusztig Theory for the General Linear and Symplectic Group. Algebras and Representation Theory, 26 (6). pp. 2819-2839. ISSN 1386-923X
Abstract
Let k be an algebraically closed field of characteristic p > 0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions involved. We give explicit constructions of left resolutions of induced modules by tilting modules. Furthermore, we give injective resolutions for induced modules in certain truncated categories. We show that the multiplicities of the indecomposable tilting and injective modules in these resolutions are the coefficients of certain Kazhdan-Lusztig polynomials. We also show that our truncated categories have a Kazhdan-Lusztig theory in the sense of Cline, Parshall and Scott. This builds further on work of Cox-De Visscher and Brundan-Stroppel.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | © The Author(s) 2023. 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. |
Keywords: | General linear group, Symplectic group, Induced modules, Tilting modules, Kazhdan-Lusztig polynomials |
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: | 06 Jan 2023 11:16 |
Last Modified: | 02 Apr 2025 14:43 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10468-022-10197-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:194794 |
Available Versions of this Item
- Injective and tilting resolutions and a Kazhdan-Lusztig theory for the general linear and symplectic group. (deposited 02 Apr 2025 14:48)