Cuspidal geometry of p-adic groups

DOI10.1007/BF02792530zbMath0634.22009MaRDI QIDQ1096728

Publication date: 1986

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Fourier transform Grothendieck group Schwartz space orthogonality relations orbital integrals tempered representations nonarchimedean local field pseudo-coefficients Selberg principle Harish- Chandra irreducible discrete series representations irreducible representations of compact groups reductive F-group Weyl integration formula

Mathematics Subject Classification ID

Analysis on (p)-adic Lie groups (22E35) Representations of Lie and linear algebraic groups over local fields (22E50) Analysis on other specific Lie groups (43A80)

Related Items (73)

Unnamed Item ⋮ An orthogonality relation for spherical characters of supercuspidal representations ⋮ On the symmetric square: orbital integrals ⋮ On the p-adic cohomology of the Lubin-Tate tower ⋮ Extensions of tempered representations ⋮ The twisted endoscopy of $GL(4)$ and $GL(5)$: Transfer of Shalika germs ⋮ Representations of groups over close local fields ⋮ Trace Paley-Wiener theorem for reductive p-adic groups ⋮ Automorphic induction for $GL(n)$ (over local nonarchimedean fields) ⋮ COMPUTATION OF A TWISTED CHARACTER OF A SMALL REPRESENTATION OF GL(3, E) ⋮ On the symmetric square: unstable local transfer ⋮ Sur les germes de Shalika pour les groupes linéaires. (On the Shalika germs for the linear groups) ⋮ Rigidity for automorphic forms ⋮ Unnamed Item ⋮ Types and unitary representations of reductive $p$-adic groups ⋮ Local character expansions and Shalika germs for GL(n) ⋮ Representation theory and sheaves on the Bruhat-Tits building ⋮ Dirac cohomology and orthogonality relations for weight modules ⋮ Unnamed Item ⋮ Cocenters and representations of affine Hecke algebras ⋮ Harish-Chandra's orthogonality relations for admissible representations ⋮ On the cuspidal support of discrete series for $p$-adic quasisplit $\mathrm{Sp}(N)$ and $\mathrm{SO}(N)$ ⋮ A spectral decomposition of orbital integrals for $PGL(2,F)$ (with an appendix by S. Debacker) ⋮ Duality in the space of tempered virtual characters of a reductive $p$-group ⋮ $\mathfrak{z}$-finite distributions on $p$-adic groups ⋮ Simple characters and coefficient systems on the building ⋮ $H^0$ of Igusa varieties via automorphic forms ⋮ On the structure of the affine asymptotic Hecke algebras ⋮ Classification of tempered representations of a non-connected $p$-adic group ⋮ Lefschetz trace formula and $\ell$-adic cohomology of Rapoport-Zink tower for $\mathrm{GSp}(4)$ ⋮ Une preuve courte du principe de Selberg pour un groupe 𝑝-adique ⋮ The Langlands-Kottwitz approach for some simple Shimura varieties ⋮ The local Langlands correspondence for $\mathrm{GL}_n$ over $p$-adic fields ⋮ The local Langlands conjecture for $\mathrm{GSp}(4)$. III: Stability and twisted endoscopy ⋮ Cocenter of $p$-adic groups. II: Induction map ⋮ On the Tempered Spectrum of Quasi-Split Classical Groups II ⋮ Characters of supercuspidal representations of classical groups ⋮ Vanishing of the leading term in Harish-Chandra’s local character expansion ⋮ Cell decomposition of some unitary group Rapoport-Zink spaces ⋮ On the tempered spectrum of quasi-split classical groups ⋮ COCENTERS OF -ADIC GROUPS, I: NEWTON DECOMPOSITION ⋮ Cocenters of $p$-adic groups. III: Elliptic and rigid cocenters ⋮ Euler-Poincaré pairing, Dirac index and elliptic pairing for Harish-Chandra modules ⋮ On local character relations ⋮ Deformation spaces of one-dimensional formal modules and their cohomology ⋮ Around the Langlands program ⋮ Projections in full $C^*$-algebras of semisimple Lie groups ⋮ Representations and quasi-characters of level $0$; endoscopy ⋮ Restriction to compact subgroups in the cyclic homology of reductive $p$-adic groups ⋮ Sur le transfert des intégrales orbitales pour les groupes linéaires (cas $p$-adique) ⋮ On the Symmetric Square: Definitions and Lemmas ⋮ On the Symmetric Square: Applications of a Trace Formula ⋮ Invariant distributions on the $n$-fold metaplectic covers of $GL(r,F)$, $F$ $p$-adic ⋮ The Schwartz algebra of an affine Hecke algebra ⋮ Regular trace formula and base change for $GL(n)$ ⋮ CUSP FORMS ON GSp(4) WITH SO(4)-PERIODS ⋮ Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families ⋮ ON THE EXISTENCE OF ADMISSIBLE SUPERSINGULAR REPRESENTATIONS OF -ADIC REDUCTIVE GROUPS ⋮ Homological algebra for affine Hecke algebras. ⋮ Unnamed Item ⋮ Metaplectic correspondence ⋮ Unnamed Item ⋮ Extensions of representations of p-adic groups ⋮ CYCLIC ODD DEGREE BASE CHANGE LIFTING FOR UNITARY GROUPS IN THREE VARIABLES ⋮ Jordan decompositions of cocenters of reductive 𝑝-adic groups ⋮ Generalized orbital integrals of some Euler-Poincaré functions of a reductive $p$-adic group ⋮ The Invariant Trace Formula. II. Global Theory ⋮ On the Kottwitz conjecture for local shtuka spaces ⋮ On elliptic tempered characters ⋮ The fundamental lemma for stable base change ⋮ The local Langlands correspondence for $\mathrm{GL}_n$ over function fields ⋮ Cyclic homology, Selberg's principle and pseudo-coefficient ⋮ On the cohomology of Kottwitz's arithmetic varieties

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