On the refined local Langlands conjecture for discrete $L$-parameters of inner forms of quasi-split disconnected real reductive groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918489008111616 |
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| author | Kaletha, Tasho Mezo, Paul |
| author_facet | Kaletha, Tasho Mezo, Paul |
| contents | Given a quasi-split connected reductive $\mathbb{R}$-group $G$ and a finite group $A$ acting on $G$ by $\mathbb{R}$-automorphisms that preserve an $\mathbb{R}$-pinning, we construct for each discrete $L$-parameter for $G$ a corresponding $L$-packet of irreducible discrete series representations on each inner forms $\tilde G_z(\mathbb{R})$ of the disconnected group $\tilde G = G \rtimes A$. We prove that these $L$-packets satisfy the endoscopic character identities with respect to normalized transfer factors. This proves the conjectural refined local Langlands correspondence for inner forms of quasi-split disconnected real reductive groups, as recently formulated by the first author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06922 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the refined local Langlands conjecture for discrete $L$-parameters of inner forms of quasi-split disconnected real reductive groups Kaletha, Tasho Mezo, Paul Representation Theory Number Theory Given a quasi-split connected reductive $\mathbb{R}$-group $G$ and a finite group $A$ acting on $G$ by $\mathbb{R}$-automorphisms that preserve an $\mathbb{R}$-pinning, we construct for each discrete $L$-parameter for $G$ a corresponding $L$-packet of irreducible discrete series representations on each inner forms $\tilde G_z(\mathbb{R})$ of the disconnected group $\tilde G = G \rtimes A$. We prove that these $L$-packets satisfy the endoscopic character identities with respect to normalized transfer factors. This proves the conjectural refined local Langlands correspondence for inner forms of quasi-split disconnected real reductive groups, as recently formulated by the first author. |
| title | On the refined local Langlands conjecture for discrete $L$-parameters of inner forms of quasi-split disconnected real reductive groups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2605.06922 |