Abstract
Previously, the last two authors found large families of decomposable Specht modules labelled by bihooks, over the Iwahori–Hecke algebra of type B. In most cases we conjectured that these were the only decomposable Specht modules labelled by bihooks, proving it in some instances. Inspired by a recent semisimplicity result of Bowman, Bessenrodt and the third author, we look back at our decomposable Specht modules and show that they are often either semisimple, or very close to being so. We obtain their exact structure and composition factors in these cases. In the process, we determine the graded decomposition numbers for almost all of the decomposable Specht modules indexed by bihooks.
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Acknowledgements
The authors thank Kay Jin Lim for useful comments about tilting modules, and Matthew Fayers, whose GAP packages were used in LLT computations as well as homomorphism computations. The authors are also grateful for the support from Singapore MOE Tier 2 AcRF MOE2015-T2-2-003, which funded a research visit of the first two authors to the third at the National University of Singapore. The second author is partially supported by JSPS Kakenhi grant number 20K22316. Finally, we thank the referees for carefully reading the paper and suggesting numerous improvements.
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Presented by: Andrew Mathas
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Muth, R., Speyer, L. & Sutton, L. Decomposable Specht Modules Indexed by Bihooks II. Algebr Represent Theor 26, 241–280 (2023). https://doi.org/10.1007/s10468-021-10093-3
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DOI: https://doi.org/10.1007/s10468-021-10093-3