Lusztig correspondence and the finite Gan-Gross-Prasad problem
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- by Zhicheng Wang;
- Trans. Amer. Math. Soc. 378 (2025), 1283-1328
- DOI: https://doi.org/10.1090/tran/9282
- Published electronically: December 4, 2024
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Abstract:
The Gan-Gross-Prasad problem is to describe the restriction of representations of a classical group $G$ to smaller groups $H$ of the same kind. In previous work by Liu and Wang [Trans. Amer. Math. Soc. 373 (2020), pp. 4223–4253; Manuscripta Math. 165 (2021), pp. 159–189; Math. Z. 297 (2021), pp. 997–1021] and Wang [Adv. Math. 393 (2021), p. 72], we study the Gan-Gross-Prasad problem for unipotent representations of finite classical groups. In this paper, we solved the Gan-Gross-Prasad problem over finite fields completely. The main tools used are the Lusztig correspondence and a formula of Reeder [J. Amer. Math. Soc. 20 (2007), pp. 573–602] for the pairings of Deligne-Lusztig characters. We give a reduction decomposition of Reeder’s formula and reduce the Gan-Gross-Prasad problem for arbitrary representations to the unipotent representations by Lusztig correspondence.References
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Bibliographic Information
- Zhicheng Wang
- Affiliation: Department of Mathematics, Jilin University, Changchun 130012, Jilin, People’s Republic of China
- Email: 11735009@zju.edu.cn
- Received by editor(s): October 9, 2022
- Received by editor(s) in revised form: May 30, 2024, and July 5, 2024
- Published electronically: December 4, 2024
- Additional Notes: The author was generously supported by the National Natural Science Foundation of PR China (No. 12201444).
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 1283-1328
- MSC (2020): Primary 20C33; Secondary 22E50
- DOI: https://doi.org/10.1090/tran/9282