{"paper":{"title":"The spectrum of the symplectic Grassmannian and $\\mathrm{Mat}_{n,m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Johannes Droschl","submitted_at":"2025-06-16T14:19:53Z","abstract_excerpt":"Let $\\mathbf{G}$ be a reductive group and $\\mathbf{X}$ a spherical $\\mathbf{G}$-variety over a local non-archimedean field $\\mathbb{F}$. We denote by $S(\\mathbf{X}(\\mathbb{F}))$ the Schwartz-functions on $\\mathbf{X}(\\mathbb{F})$. In this paper we offer a new approach on how to obtain bounds on\n  \\[\\dim_{\\mathbb{C}}\\mathrm{Hom}_{\\mathbf{G}(\\mathbb{F})}(S(\\mathbf{X}(\\mathbb{F})),\\pi)\\]for an irreducible smooth representation $\\pi$ of $\\mathbf{G}(\\mathbb{F})$. Our strategy builds on the theory of $\\rho$-derivatives and the Local Structure Theorem for spherical varieties. Currently, we focus on th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13530","kind":"arxiv","version":2},"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/2506.13530/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"}