On representations distinguished by unitary groups

DOI10.1007/s10240-012-0040-zzbMath1329.11053OpenAlexW1966456487MaRDI QIDQ691689

Brooke Feigon, Omer Offen, Erez M. Lapid

Publication date: 3 December 2012

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_2012__115__185_0/

Mathematics Subject Classification ID

Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items

Gamma factors of intertwining periods and distinction for inner forms of \(\operatorname{GL}(n)\) ⋮ A criterion for integrability of matrix coefficients with respect to a symmetric space ⋮ A nonabelian trace formula ⋮ The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case ⋮ On parabolic induction associated with a \(p\)-adic symmetric space ⋮ Periods and nonvanishing of central \(L\)-values for \(\mathrm{GL}(2n)\) ⋮ Representations of reductive groups distinguished by symmetric subgroups ⋮ A weak kernel formula for Bessel functions ⋮ The characterization of theta-distinguished representations of \(\mathrm{GL}(n)\) ⋮ The local period integrals and essential vectors ⋮ Distinction of the Steinberg representation for inner forms of \(\mathrm{GL}(n)\) ⋮ Intertwining periods and distinction forp‐adic Galois symmetric pairs ⋮ Lower bounds for Maass forms on semisimple groups ⋮ The generalized doubling method: local theory ⋮ Spherical varieties, functoriality, and quantization ⋮ On a local conjecture of Jacquet, ladder representations and standard modules ⋮ Bessel functions and Kloosterman integrals on \(\mathrm{GL}(n)\) ⋮ Test vectors for Archimedean period integrals ⋮ Multiplicity one theorems for the generalized doubling method (with an appendix by Avraham Aizenbud and Dmitry Gourevitch) ⋮ On local intertwining periods ⋮ A conjecture on Whittaker-Fourier coefficients of cusp forms ⋮ The distinction problem for metaplectic case ⋮ Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices ⋮ Automorphic period and the central value of Rankin-Selberg L-function ⋮ Klyachko models for ladder representations ⋮ Large values of cusp forms on \(\mathrm{GL}_n\) ⋮ Relative discrete series representations for two quotients of $p$-adic $\mathbf{GL}_n$ ⋮ On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad ⋮ Local unitary periods and relative discrete series ⋮ Plancherel formula for \(\mathrm{GL}_n(F)\setminus \mathrm{GL}_n(E)\) and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups ⋮ The Prasad conjectures for \(\mathrm{U}_{2}\), \(\mathrm{SO}_{4}\) and \(\mathrm{Sp}_{4}\) ⋮ Linear periods for unitary representations ⋮ A fundamental lemma for the Hecke algebra: the Jacquet-Rallis case ⋮ Supercuspidal representations of $\mathrm{GL}_{n}(F)$ distinguished by a unitary involution ⋮ On the Kohnen plus space for Hilbert modular forms of half-integral weight I

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
• The unitary dual for complex classical Lie groups
• Distinction by the quasi-split unitary group
• The de-Rham theorem and Shapiro lemma for Schwartz functions on Nash manifolds
• Generalized Harish-Chandra descent, Gelfand pairs, and an Archimedean analog of Jacquet-Rallis's theorem. With an appendix by the authors and Eitan Sayag.
• The Whittaker models of induced representations
• Trilinear forms and the central values of triple product \(L\)-functions
• Automorphic induction for \(\text{GL}(n,\mathbb C)\)
• Multiplicity one theorem for \((\text{GL}_{n+1}({\mathbb{R}}), \text{GL}_{n} ({ \mathbb{R}}))\)
• Quelques propriétés des représentations sphériques pour les espaces symétriques réductifs. (Some properties of spherical representations of reductive symmetric spaces)
• Local coefficients as Artin factors for real groups
• A trace formula for reductive groups. I: Terms associated to classes in G(Q)
• Two remarks on irreducible characters of finite general linear groups
• Spherical functions and local densities on Hermitian forms
• Meromorphic basis of \(H\)-invariant distribution vectors for generalized principal series of reductive symmetric spaces: Functional equation
• An integral transform and its applications
• Supercuspidal representations of \(\text{GL}(n)\) distinguished by a unitary subgroup
• A proof of Kirillov's conjecture
• Periods of Eisenstein series: the Galois case
• Stabilization of periods of Eisenstein series and Bessel distributions on \(GL(3)\) relative to \(U(3)\)
• A theorem of density for Kloosterman integrals
• Kloosterman identities over a quadratic extension
• \(H\)-fixed distribution vectors for generalized principal series of reductive symmetric spaces and meromorphic continuation of Eisenstein integrals
• The continuous spectrum of the relative trace formula for \(GL(3)\) over a quadratic extension
• The lifting of Kloosterman sums
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• On a conjecture of Jacquet about distinguished representations of \(\text{GL}(n)\)
• Transfer factors for Kloosterman integrals
• Automorphic induction for \(GL(n)\) (over local nonarchimedean fields)
• The fundamental lemma of Jacquet and Ye in positive characteristic
• Smooth Fréchet globalizations of Harish-Chandra modules
• On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture
• Spectral asymptotics for arithmetic quotients of \(\text{SL}(n,{\mathbb R})/\text{SO}(n)\)
• On rationality properties of involutions of reductive groups
• Unitary periods, Hermitian forms and points on flag varieties
• Kloosterman integrals for \(\mathrm{GL}(2, \mathbb R)\)
• Constant term of functions on a \(p\)-adic reductive symmetric space
• \(H\)-invariant distribution vectors of induced representations for a \(p\)-adic reductive symmetric space \(G/H\)
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Periods of Eisenstein series
• Rankin-Selberg Convolutions
• The Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129)
• Globalization of Distinguished Supercuspidal Representations of GL(n)
• Compact unitary periods
• Le spectre résiduel de ${\rm GL}(n)$
• Schwartz Functions on Nash Manifolds
• (GL_n+1(F), GL_n(F)) is a Gelfand pair for any local field F
• On the asymptotics of Whittaker functions
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• A measure on the Unipotent Variety
• On a Family of Distributions obtained from Orbits
• Kloosterman integrals and base change for GL (2).
• Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de jacquet et ye
• L-Indistinguishability For SL (2)
• Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
• On Euler Products and the Classification of Automorphic Representations I
• On Euler Products and the Classification of Automorphic Forms II
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
• Relative Kloosterman Integrals for GL(3): II
• Relative Kloosterman integrals for GL(3)
• Induced representations of reductive ${\germ p}$-adic groups. I
• On irreducibility of standard modules for generic representations
• Periods of automorphic forms
• Germs of Kloosterman Integrals for $GL(3)$
• Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)
• Distinguished representations and quadratic base change for 𝐺𝐿(3)
• Smooth transfer of Kloosterman integrals (the Archimedean case)
• Stable relative Bessel distributions on GL(n) over a quadratic extension
• ON THE FINE SPECTRAL EXPANSION OF JACQUET’S RELATIVE TRACE FORMULA
• Fonctions de Whittaker associées aux groupes de Chevalley
• Kloosterman identities over a quadratic extension II
• Smooth transfer of Kloosterman integrals
• Smooth transfer of Kloosterman integrals
• Factorization of period integrals.

This page was built for publication: On representations distinguished by unitary groups