Abstract
Let G be a connected reductive group defined over \(\mathbb{F}_q\), the finite field with q elements. Let B be a Borel subgroup defined over \(\mathbb{F}_q\). In this paper, we completely determine the composition factors of the induced module \(\mathbb{M}(\rm{tr})=\mathbb{k}G\otimes_{\mathbb{k}B}tr\) (where tr is the trivial B-module) for any field \(\mathbb{k}\).
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11501546 and 11671297). The authors are grateful to Professor Nanhua Xi for his helpful suggestions and com- ments in writing this paper. The first author thanks Professors Jianpan Wang and Naihong Hu for their advice and comments. The second author thanks Professors Toshiaki Shoji and Qiang Fu for their helpful discussion and comments.
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Chen, X., Dong, J. The decomposition of permutation module for infinite Chevalley groups. Sci. China Math. 64, 921–930 (2021). https://doi.org/10.1007/s11425-017-9532-5
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DOI: https://doi.org/10.1007/s11425-017-9532-5