The characters of discrete series as orbital integrals

DOI10.1007/BF01425569zbMath0359.22008OpenAlexW2008294301WikidataQ97993837 ScholiaQ97993837MaRDI QIDQ1238906

James Arthur

Publication date: 1976

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142372

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (31)

An infinitesimal variant of the Guo-Jacquet trace formula. I: The case of \((\mathrm{GL}_{2n, D}, \mathrm{GL}_{n, D}\times \mathrm{GL}_{n, D})\) ⋮ Generalized affine Springer fibres ⋮ New identities of differential operators from orbital integrals on 𝐺𝐿(𝑟,𝐂) ⋮ An invariant trace formula for the universal covering group of \(\text{SL}(2,\mathbb{R})\) ⋮ The local behaviour of weighted orbital integrals ⋮ The characters of supercuspidal representations as weighted orbital integrals ⋮ On the fundamental domain of affine Springer fibers ⋮ The weighted fundamental lemma. II: Cohomological statements ⋮ Germ Expansions for Real Groups ⋮ TRUNCATED AFFINE SPRINGER FIBERS AND ARTHUR’S WEIGHTED ORBITAL INTEGRALS ⋮ On the spectral side of Arthur's trace formula -- combinatorial setup ⋮ Harmonic analysis on reductive Lie groups ⋮ On a theorem of Osborne and Warner. Multiplicities in the cuspidal spectrum ⋮ A local trace formula ⋮ Vanishing results for toric varieties associated to \(\text{GL}_n\) and \(\text{G}_{2}\) ⋮ Geometric side of a local relative trace formula ⋮ On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 ⋮ On the unipotent contribution in Arthur's trace formula for general linear groups ⋮ On the homology of truncated affine Springer fibers ⋮ Unnamed Item ⋮ Parabolic transfer for real groups ⋮ Regular points in affine Springer fibers ⋮ Le lemme fondamental pondéré. I. Constructions géométriques ⋮ The spectral side of Arthur's trace formula ⋮ The \(\xi\)-stability on the affine Grassmannian ⋮ An invariant trace formula for rank one lattices ⋮ Le transfert singulier pour la formule des traces de Jacquet–Rallis ⋮ An asymptotic formula for real groups ⋮ On elliptic tempered characters ⋮ Noninvariant integrals on semisimple groups of \(\mathbb R\)-rank one ⋮ Sato-Tate equidistribution for families of automorphic representations through the stable trace formula

Cites Work

• Unnamed Item
• Harmonic analysis on real reductive groups. I: The theory of the constant term
• On the functional equations satisfied by Eisenstein series
• Discrete series for semisimple Lie groups. II: Explicit determination of the characters
• Two theorems on semi-simple Lie groups
• The Selberg trace formula for groups of F-rank one
• The Characters of Semisimple Lie Groups
• Differential Operators on a Semisimple Lie Algebra
• Fourier Transforms on a Semisimple Lie Algebra I
• A Formula for Semisimple Lie Groups
• Invariant Eigendistributions on a Semisimple Lie Group

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