{"paper":{"title":"Restriction of the metaplectic representation over a $p$-adic field to an anisotropic torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Khemais Maktouf, Pierre Torasso","submitted_at":"2025-12-04T23:28:09Z","abstract_excerpt":"In this article, we examine the restriction of the metaplectic representation $\\pi$ over a $p$-adic field $k$, $p\\neq2$, of zero characteristic to an isotropic torus $S$ contained in the symplectic group. First we give necessary and sufficient conditions on the momentum map in order that $S$ be admissible, that is $\\pi_{\\vert S}$ decomposes with finite multiplicities.\n  Let us say that a torus contained in the symplectic group is irreducible if its action on the symplectic space is irreducible over $k$. Then we examine the case when $S$ is a proper subtorus of a maximal irreducible torus $T$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.05317","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.05317/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}