Computation of the local coefficients for principal series representations of the metaplectic double cover of \(\mathrm{SL}_2(\mathbb F)\)

DOI10.1016/j.jnt.2009.01.024zbMath1245.11065OpenAlexW1978338940MaRDI QIDQ1026884

Dani Szpruch

Publication date: 6 July 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2009.01.024

zbMATH Keywords

local coefficientsWhittaker modeleven residual characteristicmetaplectic double cover of SL(2) over a local field

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items

Proofs of Ibukiyama's conjectures on Siegel modular forms of half-integral weight and of degree 2 ⋮ Distinguished theta representations for certain covering groups ⋮ Generic representations of metaplectic groups and their theta lifts ⋮ Some irreducibility theorems of parabolic induction on the metaplectic group via the Langlands-Shahidi method ⋮ The unramified computation of a Shimura integral for \(\mathrm{SL}(2)\times \mathrm{GL}(2)\) ⋮ On the existence of a \(p\)-adic metaplectic Tate-type \(\widetilde {\gamma}\)-factor ⋮ On Shahidi local coefficients matrix ⋮ Hecke \(L\)-functions and Fourier coefficients of covering Eisenstein series ⋮ Subconvex equidistribution of cusp forms: reduction to Eisenstein observables ⋮ On the Local Coefficients Matrix for Coverings of $$\mathrm{SL}_2$$SL2

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniqueness of Whittaker model for the metaplectic group
• \(p\)-adic Whittaker functions on the metaplectic group
• Twisted endoscopy and reducibility of induced representations for \(p\)- adic groups
• Weil's representation and the spectrum of the metaplectic group
• Heredity of Whittaker models on the metaplectic group
• On some explicit formulas in the theory of Weil representation
• Splitting metaplectic covers of dual reductive pairs
• The local converse theorem for \(\operatorname {SO}(2n+1)\) and applications
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• Sur certains groupes d'opérateurs unitaires
• On Certain L-Functions
• Singular Integrals and the Principal Series, IV
• The Knapp-Stein Dimension Theorem for p-Adic Groups
• On the composition series of principal series representations of a three-fold covering group of SL(2, K)
• On the theta lift from SO2n+1 to n.
• Fonctions de Whittaker associées aux groupes de Chevalley