The local Langlands correspondence for GSp_4 over local function fields

Ganapathy, Radhika

doi:10.48550/arxiv.1305.6088

Cited by 2 publications

(4 citation statements)

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“…First we do so for general linear groups over fields. The next result improves on [Gan2,Corollary 8.8] and [Gan1,Theorem 2.3.11] in the sense that it gives an explicit lower bound on the l for which the statement holds. However, our bound l > 2 n−1 r is still excessively large.…”

Section: Close Fields and Langlands Parameterssupporting

confidence: 54%

“…The special case was also proven by Ganapathy [Gan1,Gan2], but without an explicit lower bound on l.…”

Section: Introductionmentioning

confidence: 71%

“…This and the condition on the central character of π mean that all the assumptions used in the proof of [Gan2,Theorem 8.4] are fulfilled if d(σ ′ ) > 2r − 2. The result [Gan2,Theorem 8.4], which uses Proposition 4.2, says that (42…”

Section: And We Have Equality Here If and Onlymentioning

confidence: 99%

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The local Langlands correspondence for inner forms of $SL_n$

Aubert¹,

Baum²,

Plymen³

et al. 2013

Preprint

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Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SLn(F ). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SLn(F ) enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of SLn(F ) up to equivalence. An analogous result is shown in the archimedean case.To settle the case where F has positive characteristic, we employ the method of close fields. We prove that this method is compatible with the local Langlands correspondence for inner forms of GLn(F ), when the fields are close enough compared to the depth of the representations. Contents 1. Introduction 1 2. Inner forms of GL n (F ) 5 3. Inner forms of SL n (F ) 9 4. Characterization of the LLC for some representations of GL n (F ) 14 5. The method of close fields 20 6. Close fields and Langlands parameters 26 References 30

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Section: Close Fields and Langlands Parameterssupporting

confidence: 54%

“…The special case was also proven by Ganapathy [Gan1,Gan2], but without an explicit lower bound on l.…”

Section: Introductionmentioning

confidence: 71%

See 1 more Smart Citation

The local Langlands correspondence for inner forms of $SL_n$

Aubert¹,

Baum²,

Plymen³

et al. 2013

Preprint

View full text Add to dashboard Cite

show abstract

“…For GL n (F ), (1) was claimed in [Yu1,§2.3.6] and proved in [ABPS2,Proposition 4.5]. For GSp 4 (F ), (1) is proved in [Gan,§ 10]. We refer to [GrRe, Ree, ReYu] for some interesting examples of positive depth Langlands parameters and supercuspidal representations.…”

Section: Introductionmentioning

confidence: 94%