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arXiv · 2607.25127

Twisted automorphic descent to odd GSpin groups and applications

Pan Yan
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Abstract

We establish twisted automorphic descent from $(\mathrm{GL}_{2n}, \mathrm{GSpin}_2^{\delta})$, where $\mathrm{GSpin}_2^{\delta}$ is anisotropic, to the odd $\mathrm{GSpin}$ group $\mathrm{GSpin}^{\delta,\alpha}_{2n+1}$, which may be split or non-split, generalizing a construction of Jiang--Liu--Xu--Zhang. As an application, we give a new explicit construction of the global Jacquet--Langlands correspondence between $\mathrm{GL}_2$ and $D^\times$, where $D$ is a quaternion division algebra over a number field. As another application, we prove a new case of the global Gan--Gross--Prasad conjecture for $(\mathrm{GSpin}_{2n+1}, \mathrm{GSpin}^{\delta}_2)$.

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Pan Yan. 2026-07-27. Twisted automorphic descent to odd GSpin groups and applications. https://arxiv.org/abs/2607.25127

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