{"paper":{"title":"La transform\\'ee de Fourier pour les espaces tordus sur un groupe r\\'eductif $\\mathfrak{p}$-adique I. Le th\\'eor\\`eme de Paley-Wiener","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bertrand Lemaire, Guy Henniart","submitted_at":"2013-09-10T13:18:56Z","abstract_excerpt":"Let ${\\boldsymbol{G}}$ be a connected reductive group defined over a non--Archimedean local field $F$. Put $G={\\boldsymbol{G}}(F)$. Let $\\theta$ be an $F$--automorphism of ${\\boldsymbol{G}}$, and let $\\omega$ be a smooth character of $G$. This paper is concerned with the smooth complex representations $\\pi$ of $G$ such that $\\pi^\\theta=\\pi\\circ\\theta$ is isomorphic to $\\omega\\pi=\\omega\\otimes\\pi$. If $\\pi$ is admissible, in particular irreducible, the choice of an isomorphism $A$ from $\\omega\\pi$ to $\\pi^\\theta$ (and of a Haar measure on $G$) defines a distribution $\\Theta_\\pi^A={\\rm tr}(\\pi\\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2500","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}