Abstract
This article has a twofold purpose. First, by recent works of Kaletha and Loke–Ma, we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic-orthogonal case. Second, based on this description, we show that the local theta correspondence preserves distinction with respect to unramified Galois involutions.
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Acknowledgements
This work was partially supported by NSFC 11501033, Fundamental Research Funds for the Central Universities No. 14380018, and Zheng Gang Scholars Program. The author would like to thank Jia-Jun Ma for kindly answering several questions related to his paper [25] with Hung Yean Loke, and thank Wen-Wei Li for helpful comments on a preliminary version of this article. He also thanks the anonymous referee for the careful reading and helpful suggestions.
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Zhang, C. Theta lifts and distinction for regular supercuspidal representations. Math. Z. 295, 1279–1293 (2020). https://doi.org/10.1007/s00209-019-02391-w
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DOI: https://doi.org/10.1007/s00209-019-02391-w