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Jacquet modules and local Langlands correspondence

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In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them in terms of linear combinations of standard modules with rational coefficients. The main ingredient of this computation is to apply Mœglin’s explicit construction of local A-packets to tempered L-packets. Finally, we study the derivatives introduced by Mínguez.

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Acknowledgements

The author expresses gratitude to Alberto Mínguez for telling the notion of his derivatives and pointing out Proposition 6.3. Thanks are also due to the referee for the careful readings and the helpful comments.

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  1. Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan

    Hiraku Atobe

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  1. Hiraku Atobe
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Correspondence to Hiraku Atobe.

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Atobe, H. Jacquet modules and local Langlands correspondence. Invent. math. 219, 831–871 (2020). https://doi.org/10.1007/s00222-019-00918-w

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  • DOI: https://doi.org/10.1007/s00222-019-00918-w

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