On the local Langlands correspondence and Arthur conjecture for even orthogonal groups

Atobe, Hiraku; Gan, Wee Teck

doi:10.1090/ert/504

Cited by 24 publications

(40 citation statements)

References 41 publications

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“…However, following [3], their tensor product L-functions with any cuspidal automorphic representations of general linear groups are the same. We refer to Chapter 8 of [3] and Section 6 of [5] for more detailed discussion.…”

Section: 2mentioning

confidence: 99%

Arthur parameters and cuspidal automorphic modules of classical groups

Jiang

Zhang

2020

Ann. of Math. (2)

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The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain automorphic representations of general linear groups. It is a question of J. Arthur and W. Schmid that asks: How to construct concrete modules for irreducible cuspidal automorphic representations of classical groups in term of their global Arthur parameters? In this paper, we formulate a general construction of concrete modules, using Bessel periods, for cuspidal automorphic representations of classical groups with generic global Arthur parameters. Then we establish the theory for orthogonal and unitary groups, based on certain well expected conjectures. Among the consequences of the theory in this paper is that the global Gan-Gross-Prasad conjecture for those classical groups is proved in full generality in one direction and with a global assumption in the other direction.

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Section: 2mentioning

confidence: 99%

Arthur parameters and cuspidal automorphic modules of classical groups

Jiang

Zhang

2020

Ann. of Math. (2)

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“…Due to the nature of the current paper, the authors thought that it is more convenient and more direct to use the formulation in Section 2.2. In addition to the local Langlands correspondence as proved by Arthur in [4], we need the result for even special orthogonal groups as discussed by H. Atobe and W. T. Gan in [5].…”

Section: Resultsmentioning

confidence: 99%

“…Let us recall the desiderata of the weak local Langlands correspondence for even special orthogonal groups SO(V n ) from [5,Desideratum 3.2]. For the needs of this paper, we only recall some partial facts from their desiderata, which has been verified in [5], in order to fix the rationality of the local Langlands correspondence.…”

Section: 2mentioning

confidence: 99%

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Local root numbers and spectrum of the local descents for orthogonal groups : p-adic case

Jiang

Zhang

2018

Alg. Number Th.

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We investigate the local descents for special orthogonal groups over p-adic local fields of characteristic zero, and obtain explicit spectral decomposition of the local descents at the first occurrence index in terms of the local Langlands data via the explicit local Langlands correspondence and explicit calculations of relevant local root numbers. The main result can be regarded as a refinement of the local Gan-Gross-Prasad conjecture ([10]).

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“…We begin by setting down the precise hypotheses that we require. We remark that for orthogonal groups and symplectic groups, they follow from the work of Arthur [Art13] and the recent work of Atobe and Gan [AG16]. For metaplectic groups, they should eventually follow from the on-going work of Wen-Wei Li (e.g.…”

Section: Some Assumptions and Remarksmentioning

confidence: 99%

Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups

Xue¹

2017

Compositio Math.

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In this paper, we propose a conjectural identity between the Fourier–Jacobi periods on symplectic groups and the central value of certain Rankin–Selberg $L$-functions. This identity can be viewed as a refinement to the global Gan–Gross–Prasad conjecture for $\text{Sp}(2n)\times \text{Mp}(2m)$. To support this conjectural identity, we show that when $n=m$ and $n=m\pm 1$, it can be deduced from the Ichino–Ikeda conjecture in some cases via theta correspondences. As a corollary, the conjectural identity holds when $n=m=1$ or when $n=2$, $m=1$ and the automorphic representation on the bigger group is endoscopic.

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On the local Langlands correspondence and Arthur conjecture for even orthogonal groups

Cited by 24 publications

References 41 publications

Arthur parameters and cuspidal automorphic modules of classical groups

Arthur parameters and cuspidal automorphic modules of classical groups

Local root numbers and spectrum of the local descents for orthogonal groups : p-adic case

Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups

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