{"paper":{"title":"A Conjecture of Sakellaridis-Venkatesh on the Unitary Spectrum of Spherical Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Raul Gomez, Wee Teck Gan","submitted_at":"2011-11-29T05:13:56Z","abstract_excerpt":"In a recent preprint, Sakellaridis and Venkatesh considered the spectral decomposition of the space $L^2(X)$, where $X = H\\G$ is a spherical variety and $G$ is a real or $p$-adic group, and stated a conjecture describing this decomposition in terms of a dual group $\\check{G}_X$ associated to $X$. The main purpose of this paper is to verify the above conjecture in many cases when $X$, has low rank. In particular, we demonstrate this conjecture for many cases when $X$ has rank 1, and also some cases when $X$ has rank 2 or 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6694","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"}