Lusztig correspondence and the Gan-Gross-Prasad problem

Wang, Zhicheng

doi:10.48550/arxiv.2104.14473

Cited by 2 publications

(6 citation statements)

References 23 publications

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“…In this section, we consider the cuspidal case. With similar argument in Case (B), according to the main theorems in [Wang1,Wang2], we have following result. Theorem 6.16.…”

Section: Case (B)mentioning

confidence: 62%

“…In this paper, we shall prove some cases of finite fields analogy of their conjectures by known results of the finite Gan-Gross-Prasad problem [LW1,LW2,LW3,Wang1,Wang2], and calculate Kawanaka wavefront sets for some irreducible representations.…”

Section: Introductionmentioning

confidence: 90%

“…The aim of this section is to recall the descents result for irreducible representations of finite symplectic groups in [Wang1,Wang2] and calculate their (largest) descent sequence. Let π ∈ E(Sp 2n (F q ), s).…”

Section: Calculation Of Descent Sequence Indexmentioning

confidence: 99%

“…where π[a] and π ′ [−a] are defined in (4.2) and they are both unipotent representations of finite general linear groups or finite unitary groups, and m(π[a], π ′ [−a]) is defined in [Wang2,(1.2)] for unitary groups and in [Wang2,p.4] for general linear groups.…”

Section: Case (A)mentioning

confidence: 99%

“…We have explicitly described the first occurrence index in descent method in our previous work [Wang1,Wang2], and the array l(π) or partition ℓ(π) and the wavefront set of π can be calculated explicitly.…”

Section: Introductionmentioning

confidence: 99%

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Wavefront sets and descent method for finite symplectic groups

Peng¹,

Wang²

2022

Preprint

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In [JZ1], D. Jiang and L. Zhang proposed a conjecture which related the wavefront sets and the descent method in the local fields case. Recently, in [JLZ], they and D. Liu define the arithmetic wavefront set of certain irreducible admissible representation π of a classical group G(k) defined over local field k, which is a subset of k-rational nilpotent orbits of the Lie algebra of G(k), by the arithmetic structures of the enhanced L-parameter of π. These arithmetic structures are based on the rationality of the local Langlands correspondence and the local Gan-Gross-Prasad conjecture. They also prove that the arithmetic wavefront set is an invariant of π (it is independent of the choice of the Whittaker datum [JLZ, Theorem 1.1]), and propose several conjectures to describe the relationship between arithmetic wavefront sets, analytic wavefront sets and algebraic wavefront sets.In this paper we study wavefront sets of irreducible representations for finite symplectic groups and describe the relationship between wavefront sets, descent method and finite Gan-Gross-Prasad problem. The finite fields case of Gan-Gross-Prasad problem can be calculated explicitly [LW2, Wang1, Wang2]. It allows us to calculate the multiplicity of an irreducible representation in the generalised Gelfand-Graev representation corresponding to certain nilpotent orbits which are finite fields analogies of the arithmetic wavefront sets. In particular, for cuspidal representations, we give certain multiplicity one theorem and show that the finite fields analogy of arithmetic wavefront sets coincides with the wavefront sets in the sense of G. Lusztig and N. Kawanaka.

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“…In this section, we consider the cuspidal case. With similar argument in Case (B), according to the main theorems in [Wang1,Wang2], we have following result. Theorem 6.16.…”

Section: Case (B)mentioning

confidence: 62%