Comparison of the Sally-Shalika character formulas with the endoscopic character identities for $\mathrm{SL}_2$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918165863202816 |
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| author | Aubert, Anne-Marie Plymen, Roger |
| author_facet | Aubert, Anne-Marie Plymen, Roger |
| contents | We consider the depth-zero supercuspidal $L$-packets of $\mathrm{SL}_2(F)$ where $F$ is a non-archimedean local field of characteristic zero. We compare the explicit endoscopic character identities for $\mathrm{SL}_2(F)$ with the classical character formulas of Sally-Shalika. Our main result concerns the supercuspidal $L$-packet of size $4$. For this $L$-packet, we show how the norm $1$ groups $H_1, H_2, H_3$ in the three quadratic extensions of $F$ play a crucial role in the endoscopic character identities for $\mathrm{SL}_2(F)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparison of the Sally-Shalika character formulas with the endoscopic character identities for $\mathrm{SL}_2$ Aubert, Anne-Marie Plymen, Roger Representation Theory Number Theory 22E50 We consider the depth-zero supercuspidal $L$-packets of $\mathrm{SL}_2(F)$ where $F$ is a non-archimedean local field of characteristic zero. We compare the explicit endoscopic character identities for $\mathrm{SL}_2(F)$ with the classical character formulas of Sally-Shalika. Our main result concerns the supercuspidal $L$-packet of size $4$. For this $L$-packet, we show how the norm $1$ groups $H_1, H_2, H_3$ in the three quadratic extensions of $F$ play a crucial role in the endoscopic character identities for $\mathrm{SL}_2(F)$. |
| title | Comparison of the Sally-Shalika character formulas with the endoscopic character identities for $\mathrm{SL}_2$ |
| topic | Representation Theory Number Theory 22E50 |
| url | https://arxiv.org/abs/2410.20183 |