Epipelagic $$L$$ L -packets and rectifying characters

Kaletha, Tasho

doi:10.1007/s00222-014-0566-4

Cited by 50 publications

(42 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…cit. ), which generalizes previous works [Ree08, DR09, DR10, Kal14, RY14,Kal15]. Hence it is natural to ask for a description of the local theta correspondence between regular supercuspidal representations in terms of tame regular elliptic pairs, which will in turn reflect the relation between the Lparameters under theta lifts.…”

Section: Introductionsupporting

confidence: 62%

Theta lifts and distinction for regular supercuspidal representations

Zhang

2019

Math. Z.

View full text Add to dashboard Cite

show abstract

Section: Introductionsupporting

confidence: 62%

Theta lifts and distinction for regular supercuspidal representations

Zhang

2019

Math. Z.

View full text Add to dashboard Cite

show abstract

“…The two ways of identifying X w (M ) with (Z( M ) I ) Φ , that via the Kottwitz isomorphism and that via Langlands duality, agree. 2 For a more general result which implies this agreement, see [Kal,Prop. 4.5.2].…”

Section: Review Of the Bernstein Centermentioning

confidence: 69%

The stable Bernstein center and test functions for Shimura varieties

Haines

2014

Automorphic Forms and Galois Representations

View full text Add to dashboard Cite

We elaborate the theory of the stable Bernstein center of a p-adic group G, and apply it to state a general conjecture on test functions for Shimura varieties due to the author and R. Kottwitz. This conjecture provides a framework by which one might pursue the Langlands-Kottwitz method in a very general situation: not necessarily PEL Shimura varieties with arbitrary level structure at p. We give a concrete reinterpretation of the test function conjecture in the context of parahoric level structure. We also use the stable Bernstein center to formulate some of the transfer conjectures (the "fundamental lemmas") that would be needed if one attempts to use the test function conjecture to express the local Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions.

show abstract

“…We mention some prior results confirming the formal degree conjecture for inner forms of GL n and SL n [HII08b], unipotent discrete series representations of adjoint unramified groups [Ree00, CKK12, Opd13], depth-zero supercuspidal representations of pure inner forms of unramified groups [DR09], [HII08b,§3.5], and certain positive-depth supercuspidal representations of tamely ramified groups [GR10, RY14,Kal12]. The formal degree conjecture is also known for U(3), GSp 2 , Sp 2 [GI14], and Mp 1 [Qiu12].…”

Section: Introductionmentioning

confidence: 79%

On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups

Ichino¹,

Lapid²,

Mao³

2017

Duke Math. J.

View full text Add to dashboard Cite

Abstract. The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint γ-factor of its L-parameter. In this paper, we prove the formal degree conjecture for odd special orthogonal and metaplectic groups in the generic case, which combined with Arthur's work on the local Langlands correspondence implies the conjecture in full generality.

show abstract

Epipelagic $$L$$ L -packets and rectifying characters

Cited by 50 publications

References 46 publications

Theta lifts and distinction for regular supercuspidal representations

Theta lifts and distinction for regular supercuspidal representations

The stable Bernstein center and test functions for Shimura varieties

On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups

Contact Info

Product

Resources

About