Non-zero condition on Mœglin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908375771512832 |
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| author | Huang, Chang |
| author_facet | Huang, Chang |
| contents | Mœglin-Renard parametrized A-packet of unitary group through cohomological induction in good parity case. Each parameter gives rise to an $A_{\mathfrak q}(λ)$ which is either $0$ or irreducible. Trapa proposed an algorithm to determine whether a ``mediocre'' $A_{\mathfrak q}(λ)$ of $\mathrm U(p, q)$ is non-zero. Based on his result, we present a further understanding of the non-zero condition on Mœglin-Renard's parametrization. Our criterion comes out to be a system of linear constraints, and has the same formulation as $p$-adic case. This suggests a map from A-packets of real unitary group to A-packets of $p$-adic symplectic group or special orthogonal group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-zero condition on Mœglin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$ Huang, Chang Representation Theory Mœglin-Renard parametrized A-packet of unitary group through cohomological induction in good parity case. Each parameter gives rise to an $A_{\mathfrak q}(λ)$ which is either $0$ or irreducible. Trapa proposed an algorithm to determine whether a ``mediocre'' $A_{\mathfrak q}(λ)$ of $\mathrm U(p, q)$ is non-zero. Based on his result, we present a further understanding of the non-zero condition on Mœglin-Renard's parametrization. Our criterion comes out to be a system of linear constraints, and has the same formulation as $p$-adic case. This suggests a map from A-packets of real unitary group to A-packets of $p$-adic symplectic group or special orthogonal group. |
| title | Non-zero condition on Mœglin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2409.09358 |