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On Local Descent to Metaplectic Groups and Local Theta Correspondence

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Abstract

Let F be a p-adic field of characteristic 0. We study a twisted local descent construction for the metaplectic groups \(\widetilde{\text{Sp}}_{2n}(F)\), and also its relation to the corresponding local descent construction for odd special orthogonal groups via local theta correspondence. In consequence, we show that this descent construction gives irreducible supercuspidal genuine representations of \(\widetilde{\text{Sp}}_{2n}(F)\) parametrized by a simple local L-parameter φτ corresponding to an irreducible supercuspidal representation τ of GL2n(F) of symplectic type, and the genericity of the representations constructed can be indicated by a local epsilon factor condition. In particular, this local descent construction recovers the local Shimura correspondence for supercuspidal representations.

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Acknowledgements

We thank the referee for both the careful reading of the manuscript and the helpful comments.

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  1. School of Mathematics, Sichuan University, Chengdu, 610064, P. R. China

    Bin Xu

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Xu, B. On Local Descent to Metaplectic Groups and Local Theta Correspondence. Acta. Math. Sin.-English Ser. 37, 142–172 (2021). https://doi.org/10.1007/s10114-020-8422-5

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