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Depth-preserving property of the local Langlands correspondence for quasi-split classical groups in large residual characteristic

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Abstract

For a quasi-split classical group over a p-adic field with sufficiently large residual characteristic, we prove that the maximum depth of a representation in each L-packet equals the depth of the corresponding L-parameter. Furthermore, for quasi-split unitary groups, we show that the depth is constant in each L-packet. The key is an analysis of the endoscopic character relation via harmonic analysis based on Bruhat–Tits theory. These results are slight generalizations of a result of Ganapathy and Varma.

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Acknowledgements

The author would like to thank his advisor Yoichi Mieda for his support and encouragement. The author also expresses his sincere gratitude to the anonymous referees for their carefully reading of this paper and for giving the author a lot of constructive and valuable suggestions. This work was carried out with the support from the Program for Leading Graduate Schools, MEXT, Japan. This work was also supported by JSPS Research Fellowship for Young Scientists and KAKENHI Grant Number 17J05451.

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  1. Department of Mathematics (Hakubi center), Kyoto University, Kitashirakawa, Oiwake-cho, Sakyo-ku,Kyoto, 606-8502, Japan

    Masao Oi

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Correspondence to Masao Oi.

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Oi, M. Depth-preserving property of the local Langlands correspondence for quasi-split classical groups in large residual characteristic. manuscripta math. 171, 529–562 (2023). https://doi.org/10.1007/s00229-022-01397-9

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