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arXiv · 2502.00781

Spectral transfer for metaplectic groups. II. Hecke algebra correspondences

Fei Chen·Wen-Wei Li
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Abstract

Let $\mathrm{Mp}(2n)$ be the metaplectic group over a local field $F \supset \mathbb{Q}_p$ defined by an additive character of $F$ of conductor $4\mathfrak{o}_F$. Gan-Savin ($p \neq 2$) and Takeda-Wood ($p=2$) obtained an equivalence between the Bernstein block of $\mathrm{Mp}(2n)$ containing the even (resp. odd) Weil representation and the Iwahori-spherical block of the split $\mathrm{SO}(2n+1)$ (resp. its non-split inner form), by giving an isomorphism between Hecke algebras. We revisit this equivalence from an endoscopic perspective. It turns out that the L-parameters of irreducible representations are preserved, whilst the difference between characters of component groups is governed by symplectic local root numbers.

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Fei Chen, Wen-Wei Li. 2025-09-10. Spectral transfer for metaplectic groups. II. Hecke algebra correspondences. https://doi.org/10.1007/s42543-025-00111-4

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