Abstract
Let \( G=\operatorname{GL}_{n}() \) be the real general linear group. By employing Borel’s lemma and Schwartz inductions for Nash groups, we give an upper bound for the weights of the Jacquet module of the principal series representations of \( G \).
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Acknowledgments
This work was an outcome of an idea of Binyong Sun and helpful discussions with Zhanqiang Bai and Dongwen Liu during the author’s visit to the Institute of Advanced Study of Mathematics in Zhejiang University. The author thanks them and also the hospitality of the Institute during the visit.
Funding
This work was supported in part by the Fundamental Research Funds for the Central Universities (Grant no. JUSRP121045) and the Natural Science Foundation of the Jiangsu Province (Grant no. BK20221057).
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Chen, Y. Estimate of the Weights of the Jacquet Module of the Principal Series Representations of \( \operatorname{GL}_{n}() \). Sib Math J 64, 1035–1042 (2023). https://doi.org/10.1134/S0037446623040237
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DOI: https://doi.org/10.1134/S0037446623040237