Abstract
Let k be an algebraically closed field of prime characteristic p and P a finite p-group. We compute the Scott kG-module with vertex P when \(\mathcal {F}\) is a constrained fusion system on P and G is Park’s group for \(\mathcal {F}\). In the case that \(\mathcal {F}\) is a fusion system of the quadratic group \(\operatorname {Qd}(p)=(\mathbb {Z}/p\times \mathbb {Z}/p)\rtimes {\text {SL}}(2,p)\) on a Sylow p-subgroup P of Qd(p) and G is Park’s group for \(\mathcal {F}\), we prove that the Scott kG-module with vertex P is Brauer indecomposable.
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Acknowledgements
The authors would like to thank the referees for their careful reading of the first manuscript and for valuable comments. A part of this work was done while the second author was visiting Chiba University in July 2017. She would like to thank the Center for Frontier Science, Chiba University for their hospitality. She would like to thank also Naoko Kunugi for her hospitality.
Funding
The first author was supported in part by the Japan Society for Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C)15K04776, 2015–2018. The second author was partially supported by the Center for Frontier Science, Chiba University and Mimar Sinan Fine Arts University Scientific Research Project Unit with project number 2017/22.
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Presented by: Radha Kessar
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Koshitani, S., Tuvay, İ. The Brauer Indecomposability of Scott Modules for the Quadratic Group Qd(p). Algebr Represent Theor 22, 1387–1397 (2019). https://doi.org/10.1007/s10468-018-9825-1
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DOI: https://doi.org/10.1007/s10468-018-9825-1