{"paper":{"title":"Global representations of the Heat and Schr\\\"odinger equation with singular potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jose Franco, Mark Sepanski","submitted_at":"2011-10-05T16:05:54Z","abstract_excerpt":"We study the $n$-dimensional Schr\\\"odinger equation with singular potential $V_\\lambda(x)=\\lambda |x|^{-2}$. Its solution space is studied as a global representation of $\\widetilde{SL(2,\\R)}\\times O(n)$. A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of $K$-finite vectors is calculated, obtaining conditions for $\\lambda$ so that this space is non-empty. The direct sum of solution spaces, over such admissible values of $\\lambda$ is studied as a representation of the $2n+1$-dimensional Heisenberg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1030","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":""},"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"}