Spectral transfer for metaplectic groups. II. Hecke algebra correspondences
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908586511171584 |
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| author | Chen, Fei Li, Wen-Wei |
| author_facet | Chen, Fei Li, Wen-Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00781 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral transfer for metaplectic groups. II. Hecke algebra correspondences Chen, Fei Li, Wen-Wei Representation Theory 22E50 (Primary) 11F70, 20C08 (Secondary) 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. |
| title | Spectral transfer for metaplectic groups. II. Hecke algebra correspondences |
| topic | Representation Theory 22E50 (Primary) 11F70, 20C08 (Secondary) |
| url | https://arxiv.org/abs/2502.00781 |