The Langlands classification and irreducible characters for real reductive groups

zbMath0756.22004MaRDI QIDQ1189557

Dan Barbasch, Jeffrey D. Adams, David A. jun. Vogan

Publication date: 18 September 1992

Published in: Progress in Mathematics (Search for Journal in Brave)

automorphic forms irreducible representations local field Cartan subgroups projective representations perverse sheaves \(p\)-adic fields reductive algebraic group Whittaker models Harish-Chandra modules complex dual group space of \(p\)-adic Langlands parameters

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) Langlands-Weil conjectures, nonabelian class field theory (11S37) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) Research exposition (monographs, survey articles) pertaining to topological groups (22-02)

Related Items (63)

On Baxter \({\mathcal Q}\)-operators and their arithmetic implications ⋮ Differential equations and Lie group representations ⋮ Arthur packets for 𝑝-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples ⋮ The Langlands classification of representations having integral regular infinitesimal characters of the classical groups of type \(A_ n\), \(B_ n\), and \(C_ n^*\) ⋮ Ordre de Bruhat et transfert : le cas réel ⋮ Representations associated to small nilpotent orbits for complex Spin groups ⋮ Global rigid inner forms and multiplicities of discrete automorphic representations ⋮ Rigid inner forms of real and \(p\)-adic groups ⋮ Loop spaces and representations ⋮ Boundary values of holomorphic functions, singular unitary representations of \(O(p,q)\), and their limits as \(q\to\infty\) ⋮ The characteristic cycles and semi-canonical bases on type \(A\) quiver variety ⋮ Level one algebraic cusp forms of classical groups of small rank ⋮ Unnamed Item ⋮ The Local Langlands Conjectures for Non-quasi-split Groups ⋮ Automorphic functions on moduli spaces of bundles on curves over local fields: a survey ⋮ Representations of reductive groups over local fields ⋮ Proof of Vogan's conjecture on Arthur packets: irreducible parameters of \(p\)-adic general linear groups ⋮ Séries discrètes des espaces symétriques et paquets d’Arthur ⋮ Rigid inner forms over local function fields ⋮ Unipotent representations and microlocalization ⋮ On the variety of Lagrangian subalgebras, I ⋮ L-packets over strong real forms ⋮ Character \(D\)-modules via Drinfeld center of Harish-Chandra bimodules. ⋮ Enveloping algebras and geometric representation theory. Abstracts from the workshop held October 31 -- November 6, 2021 (hybrid meeting) ⋮ Endoscopic character identities for metaplectic groups ⋮ Koszul Duality Patterns in Representation Theory ⋮ Some consequences of Arthur's work on the spectrum and topology of hyperbolic varieties ⋮ Lifting of characters on orthogonal and metaplectic groups ⋮ A generalization of Duflo's conjecture ⋮ Characteristic cycles for the loop Grassmannian and nilpotent orbits. ⋮ On the transfer of distributions: Weighted orbital integrals ⋮ Paquets d’Arthur des groupes classiques complexes ⋮ Geometric parameters corresponding to representations of the classical groups with integral infinitesimal characters ⋮ The unitary spherical spectrum for split classical groups ⋮ Algebraic families of groups and commuting involutions ⋮ SUR LES PAQUETS D’ARTHUR DE CONTENANT DES MODULES UNITAIRES DE PLUS HAUT POIDS, SCALAIRES ⋮ Koszul duality for quasi-split real groups ⋮ Lifting of characters for nonlinear simply laced groups ⋮ Dirac index and twisted characters ⋮ Rigid inner forms vs isocrystals ⋮ Unnamed Item ⋮ Unipotent representations attached to the principal nilpotent orbit ⋮ Real forms of \({\mathcal U}_ q({\mathfrak g})\) ⋮ On the combinatorics of unramified admissible modules ⋮ Unnamed Item ⋮ Galois and Cartan cohomology of real groups ⋮ Arthur packets and the Ramanujan conjecture ⋮ Automorphic induction for \(\text{GL}(n,\mathbb C)\) ⋮ Paquets d’Arthur des groupes classiques et unitaires ⋮ Categorical Langlands correspondence for 𝑆𝑂_{𝑛,1}(ℝ) ⋮ Pseudo-real principalG-bundles over a real curve ⋮ Tempered endoscopy for real groups III: Inversion of transfer and 𝐿-packet structure ⋮ Equivariant deformation quantization and coadjoint orbit method ⋮ Algorithms for representation theory of real reductive groups ⋮ Non-cuspidal square integrable automorphic forms. ⋮ Unnamed Item ⋮ Parameters for twisted representations ⋮ Arthur packets for \(G_2\) and perverse sheaves on cubics ⋮ Howe correspondence for real unitary groups ⋮ Reducible characteristic cycles of Harish-Chandra modules for U(p,q) and the Kashiwara–Saito singularity ⋮ Some geometric facets of the Langlands correspondence for real groups ⋮ Unipotent ideals for spin and exceptional groups ⋮ Characteristic cycles, micro local packets and packets with cohomology

This page was built for publication: The Langlands classification and irreducible characters for real reductive groups