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arXiv · 2411.03091

Variation of additive characters in the transfer for Mp(2n)

Wen-Wei Li
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Abstract

Let $\mathrm{Mp}(2n)$ 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 $\mathrm{Mp}(2n)$ 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 $\mathrm{Mp}(2n)$ depends on the additive characters.

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BibTeXRIS

Wen-Wei Li. 2024-11-05. Variation of additive characters in the transfer for Mp(2n). https://arxiv.org/abs/2411.03091

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