The local Langlands correspondence for GSp 4 over local function fields

Ganapathy, Radhika

doi:10.1353/ajm.2015.0045

Cited by 19 publications

(68 citation statements)

References 47 publications

(145 reference statements)

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“…The special case was also proven by Ganapathy [20,21], but without an explicit lower bound on l. Theorem 1.3 says that the method of close fields essentially preserves Langlands parameters. The proof runs via the only accessible characterization of the LLC for general linear groups: by means of -and γ -factors of pairs of representations [27].…”

Section: Introductionmentioning

confidence: 80%

“…which is a condition needed for [21,Theorem 7.5]. Its other conditions are among our assumptions, so from [21, Theorem 7.5] we see that indeed φ = rec F,n (π).…”

Section: Suppose That Det φ Corresponds To the Central Character Of πmentioning

confidence: 88%

“…In the case d(σ ) > 2r − 2, this is the content of [21,Theorem 7.4]. We note that this result uses both the assumption on the central character of π and Proposition 4.2.…”

Section: Suppose That Det φ Corresponds To the Central Character Of πmentioning

confidence: 89%

“…Since G/G Z(G) is an abelian group and all its elements have order dividing n, the same goes for X G ( φ (G)). Moreover, X G ( φ (G)) is finite, as we will see in (21). On general grounds [29, Lemma 2.4], there exists a 2-cocycle κ φ such that…”

Section: Inner Forms Of Sl N (F)mentioning

confidence: 91%

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The local Langlands correspondence for inner forms of SL$$_{n}$$

et al. 2016

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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 SL n (F). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SL n (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 SL n (F) up to equivalence. An analogous result is shown in the archimedean case. For p-adic fields, this is based on the work of Hiraga and Saito. 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 GL n (F), when the fields are close enough compared to the depth of the representations.

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Section: Introductionmentioning

confidence: 80%

“…which is a condition needed for [21,Theorem 7.5]. Its other conditions are among our assumptions, so from [21, Theorem 7.5] we see that indeed φ = rec F,n (π).…”

Section: Suppose That Det φ Corresponds To the Central Character Of πmentioning

confidence: 88%

“…In the case d(σ ) > 2r − 2, this is the content of [21,Theorem 7.4]. We note that this result uses both the assumption on the central character of π and Proposition 4.2.…”

Section: Suppose That Det φ Corresponds To the Central Character Of πmentioning

confidence: 89%

Section: Inner Forms Of Sl N (F)mentioning

confidence: 91%

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The local Langlands correspondence for inner forms of SL$$_{n}$$

et al. 2016

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“…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%

Depth and the Local Langlands Correspondence

Aubert

Baum

Plymen

et al. 2016

Arbeitstagung Bonn 2013

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Local Langlands and Springer Correspondences

Aubert

2019

Progress in Mathematics

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This notes are the written version of a course given by the author at the workshop "Representation theory of p-adic groups" that was held at IISER Pune, India, in July 2017 (to appear in Representations of p-adic groups: Contributions from Pune, Progress in Math., Birkhäuser). They give notably an overview of results obtained jointly with Ahmed Moussaoui and Maarten Solleveld on the local Langlands correspondence, focusing on the links of the latter with both the generalized Springer correspondence and the geometric conjecture, the so-called ABPS Conjecture, introduced in collaboration with Paul Baum, Roger Plymen and Maarten Solleveld. Langlands parameters correspond by the LLC to the irreducible supercuspidal representations of G. The validity of this conjecture is proved for representations with unipotent reduction of the group G of the F-rational points of any connected reductive algebraic group which splits over an unramified extension of F in [FOS, Theorem 2] (when G is simple of adjoint type it is a special case of [Lus4], [Lus5]), for the Deligne-Lusztig depth-zero supercuspidal representations (as a consequence of [DeRe]), and also for general linear groups and split classical p-adic groups (any representation) (see [Mou1]), for inner forms of linear groups and of special linear groups, and for quasi-split unitary p-adic groups (any representation) (see [AMS1, § 6]).

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The local Langlands correspondence for GSp 4 over local function fields

Abstract: We prove the local Langlands correspondence for GSp 4 (F ), where F is a non-archimedean local field of positive characteristic with residue characteristic > 2.

Cited by 19 publications

References 47 publications

The local Langlands correspondence for inner forms of SL$$_{n}$$

The local Langlands correspondence for inner forms of SL$$_{n}$$

Depth and the Local Langlands Correspondence

Local Langlands and Springer Correspondences

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