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<p>Let Mp(2<i>n</i>) be the metaplectic group of rank <i>n</i> over a local field <i>F</i> of characteristic zero. In this note, we determine the behavior of endoscopic transfer for Mp(2<i>n</i>) under variation of additive characters of <i>F</i>. The arguments are based on properties of transfer factor, requiring no deeper results from representation theory. Combined with the endoscopic character relations of Luo, this provides a simple and uniform proof of a theorem of Gan–Savin, which describes how the local Langlands correspondence for Mp(2<i>n</i>) depends on the additive characters.</p>

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Variation of Additive Characters in the Transfer for Mp(2n)

  • 期刊论文

  • 发表日期：

    2026年3月20日

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  • Wen-Wei Li

摘要

Let Mp(2n) be the metaplectic group of rank n over a local field F of characteristic zero. In this note, we determine the behavior of endoscopic transfer for Mp(2n) under variation of additive characters of F. The arguments are based on properties of transfer factor, requiring no deeper results from representation theory. Combined with the endoscopic character relations of Luo, this provides a simple and uniform proof of a theorem of Gan–Savin, which describes how the local Langlands correspondence for Mp(2n) depends on the additive characters.