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arXiv · 2409.09358

Non-zero condition on Mœglin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$

Chang Huang
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Abstract

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.

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Chang Huang. 2025-05-23. Non-zero condition on Mœglin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$. https://arxiv.org/abs/2409.09358

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