Whittaker supports for representations of reductive groups

DOI10.5802/aif.3372OpenAlexW3157008513MaRDI QIDQ2034715

Yanyan Li

Publication date: 22 June 2021

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.00284

zbMATH Keywords

Heisenberg grouposcillator representationautomorphic formFourier coefficientcuspidal representationmetaplectic groupwave-front setdistinguished orbitadmissible orbit

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)

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On the wavefront sets associated with theta representations, Quaternionic Speh representations, Geometric wave-front set may not be a singleton, Local Rankin–Selberg integrals for Speh representations, Multiplicity one theorems for the generalized doubling method (with an appendix by Avraham Aizenbud and Dmitry Gourevitch), Doubling constructions and tensor product \(L\)-functions: the linear case, A generalized Theta lifting, CAP representations, and Arthur parameters, Eulerianity of Fourier coefficients of automorphic forms, Annihilator varieties of distinguished modules of reductive Lie algebras, 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

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