Some irreducibility theorems of parabolic induction on the metaplectic group via the Langlands-Shahidi method

Szpruch, Dani

doi:10.1007/s11856-012-0140-y

Cited by 26 publications

(25 citation statements)

References 38 publications

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“…This is Rodier's result for linear groups (see [11,Corollary 1.7]), which is extended by Banks [7] to a non-algebraic setting. When r = 1, Lemma follows from the definition of γ Sh (s, τ × π 0 , ψ) and [43,Theorem B]. In general, Lemma follows from a standard argument similar to [38, Theorem 2.1.1, Proposition 3.2.1].…”

Section: Appendix B Some Results On Representations Of Metaplectic Gmentioning

confidence: 99%

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The local theta correspondence and the local Gan–Gross–Prasad conjecture for the symplectic-metaplectic case

Atobe

2017

Math. Ann.

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Section: Appendix B Some Results On Representations Of Metaplectic Gmentioning

confidence: 99%

“…, s r ), τ 1 × · · · × τ r ⋊ π 0 , w) is finite. When r = 1 and π 0 is w ′ 1 -generic, Szpruch [43] defined a gamma factor γ Sh (s 1 , τ 1 × π 0 , ψ) by γ Sh (s 1 , τ 1 × π 0 , ψ) = C Sp(W2n) ψ (s 1 , τ 1 ⋊ π 0 , w n )…”

Section: Appendix B Some Results On Representations Of Metaplectic Gmentioning

confidence: 99%

The local theta correspondence and the local Gan–Gross–Prasad conjecture for the symplectic-metaplectic case

Atobe

2017

Math. Ann.

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“…This uniqueness plays pivotal role in the work of Szpruch (cf. [Szp1]- [Szp4]) generalizing the method of Langlands-Shahidi to Sp (2) 2r . Besides this special family of examples, the uniqueness of Whittaker functionals fails widely, and one almost never expects such uniform property for all genuine representations of a general covering group.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Distinguished theta representations for certain covering groups

Gao

2017

Pacific J. Math.

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Abstract. For Brylinski-Deligne covering groups of an arbitrary split reductive group, we consider theta representations attached to certain exceptional genuine characters. The goal of the paper is to study the dimension of the space of Whittaker functionals of a theta representation. In particular, we investigate when the dimension is exactly one, in which case the theta representation is called distinguished. For this purpose, we first give effective lower and upper bounds for the dimension of Whittaker functionals for general theta representations. As a consequence, the dimension in many cases can be reduced to simple combinatorial computations, e.g., the Kazhdan-Patterson covering groups of the general linear groups, or covering groups whose complex dual groups (à la Finkelberg-Lysenko-McNamara-Reich) are of adjoint type. In the second part of the paper, we consider coverings of certain semisimple simply-connected groups and give necessary and sufficient condition for the theta representation to be distinguished. There are subtleties arising from the relation between the rank and the degree of the covering group. However, in each case we will determine the exceptional character such that its associated theta representation is distinguished.

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“…Moreover, in [12] Li assumed the theory of R-groups for Sp 2n (F ), the metaplectic double cover of Sp 2n (F ) which is based on the Knapp-Stein Dimension Theorem. Assuming the Knapp-Stein Dimension Theorem, it was proven in [22] that all genuine principal representations of Sp 2n (F ) induced from a unitary character are irreducible. This result was proved unconditionally in [9].…”

Section: An Irreducibility Resultmentioning

confidence: 99%

Plancherel measures for coverings of p-adic SL2(F)

Goldberg

Szpruch

2016

Int. J. Number Theory

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In these notes we compute the Plancherel measures associated with genuine principal series representations of n-fold covers of p−adic SL 2 . Along the way we also compute a higher dimensional metaplectic analog of Shahidi local coefficients. Our method involves new functional equations utilizing the Tate γ-factor and a metaplectic counterpart. As an application we prove an irreducibility theorem.

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Some irreducibility theorems of parabolic induction on the metaplectic group via the Langlands-Shahidi method

Cited by 26 publications

References 38 publications

The local theta correspondence and the local Gan–Gross–Prasad conjecture for the symplectic-metaplectic case

The local theta correspondence and the local Gan–Gross–Prasad conjecture for the symplectic-metaplectic case

Distinguished theta representations for certain covering groups

Plancherel measures for coverings of p-adic SL2(F)

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