Parker, A orcid.org/0000-0001-7014-6150 (2008) Some remarks on a result of Jensen and tilting modules for $\SL_3(k)$ and $q$-$\GL_3(k)$. [Preprint - arXiv]
Abstract
This paper reviews a result of Jensen on characters of some tilting modules for $\SL_3(k)$, where k has characteristic at least five and fills in some gaps in the proof of this result. We then apply the result to finding some decomposition numbers for three part partitions for the symmetric group and the Hecke algebra. We review what is known for characteristic two and three. The quantum case is also considered: analogous results hold for the mixed quantum group where q is an lth root of unity with l at least three and thus also hold for the associated Hecke algebra.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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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: | 30 Oct 2024 15:19 |
Last Modified: | 30 Oct 2024 15:19 |
Identification Number: | 10.48550/arXiv.0809.2249 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:150293 |