Generalized and degenerate Whittaker models

DOI10.1112/S0010437X16007788zbMath1384.20039arXiv1502.06483OpenAlexW3101572523MaRDI QIDQ5360266

No author found.

Publication date: 28 September 2017

Full work available at URL: https://arxiv.org/abs/1502.06483

zbMATH Keywords

Heisenberg groupreductive grouposcillator representationwave-front setBernstein-Zelevinsky derivativeWhittaker-Fourier coefficient

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Semisimple Lie groups and their representations (22E46) Linear algebraic groups over global fields and their integers (20G30) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Representations of Lie and linear algebraic groups over local fields (22E50) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55) Linear algebraic groups over local fields and their integers (20G25) Linear algebraic groups over adèles and other rings and schemes (20G35) Coadjoint orbits; nilpotent varieties (17B08)

Related Items (22)

On the wavefront sets associated with theta representations ⋮ The generalized doubling method: (𝑘,𝑐) models ⋮ Fourier coefficients for degenerate Eisenstein series and the descending decomposition ⋮ Twisted doubling integrals for classical groups ⋮ Quaternionic Speh representations ⋮ On automorphic descent from \(GL_7\) to \(G_2\) ⋮ A triangular system for local character expansions of Iwahori-spherical representations of general linear groups ⋮ Local Rankin–Selberg integrals for Speh representations ⋮ TWISTED DOUBLING INTEGRALS FOR BRYLINSKI–DELIGNE EXTENSIONS OF CLASSICAL GROUPS ⋮ The generalized doubling method: local theory ⋮ Automorphic descent for symplectic groups: The branching problems and L -functions ⋮ A reciprocal branching problem for automorphic representations and global Vogan packets ⋮ Local descent to quasi-split even general spin groups ⋮ Multiplicity one theorems for the generalized doubling method (with an appendix by Avraham Aizenbud and Dmitry Gourevitch) ⋮ On top Fourier coefficients of certain automorphic representations of \(\mathrm{GL}_n\) ⋮ Fourier coefficients attached to small automorphic representations of \(\operatorname{SL}_n(\mathbb{A})\) ⋮ Whittaker supports for representations of reductive groups ⋮ Doubling constructions and tensor product \(L\)-functions: the linear case ⋮ Eulerianity of Fourier coefficients of automorphic forms ⋮ Degenerate principal series and nilpotent invariants ⋮ A reduction principle for Fourier coefficients of automorphic forms ⋮ Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Primitive ideals and orbital integrals in complex exceptional groups
• On the associated variety of a primitive ideal
• Modèles de Whittaker dégénéres pour des groupes p-adiques. (Degenerate Whittaker models of p-adic groups)
• Whittaker vectors and associated varieties
• The local structure of characters
• Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, II
• La conjecture de Weil. II
• Primitive ideals and orbital integrals in complex classical groups
• Characters, dual pairs, and unipotent representations
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• Gelfand-Kirillov dimension for Harish-Chandra modules
• On Whittaker vectors and representation theory
• A proof of Kirillov's conjecture
• Characteristic cycles and wave front cycles of representations of reductive Lie groups
• Differential operators on homogeneous spaces. I: Irreducibility of the associated variety for annihilators of induced modules
• Picard-Lefschetz theory and characters of a semisimple Lie group
• Annihilator varieties, adduced representations, Whittaker functionals, and rank for unitary representations of \(GL(n)\)
• Derivatives for smooth representations of \(\mathrm{GL}(n, \mathbb R)\) and \(\mathrm{GL}(n, \mathbb C)\)
• Twisted homology for the mirabolic nilradical
• Certain conjectures relating unipotent orbits to automorphic representations
• On a result of Moeglin and Waldspurger in residual characteristic 2
• Local theta lifting of generalized Whittaker models associated to nilpotent orbits
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Tempered representations and nilpotent orbits
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• Model Transition for Representations of Metaplectic Type
• Canonical Extensions of Harish-Chandra Modules to Representations of G
• Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
• Sur les représentations différentiables des groupes de Lie algébriques
• Induced representations of reductive ${\germ p}$-adic groups. I
• On a correspondence between cuspidal representations of 𝐺𝐿_{2𝑛} and 𝑆𝑝̃_{2𝑛}
• Generalized Whittaker models and the Bernstein center
• $C^{-\infty}$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations
• Invariants and -spectrums of local theta lifts
• Degenerate Whittaker functionals for real reductive groups
• Raising nilpotent orbits in wave-front sets
• Des catégories abéliennes
• Front d'onde des representations des groupes classiques p -adiques
• On Whittaker vectors for generalized Gelfand-Graev representations of semisimple Lie groups

This page was built for publication: Generalized and degenerate Whittaker models