{"paper":{"title":"Local equivalence of representations of Diff$^+(S^1)$ corresponding to different highest weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","math.RT"],"primary_cat":"math-ph","authors_text":"Mih\\'aly Weiner","submitted_at":"2016-06-01T16:14:48Z","abstract_excerpt":"Let $c,h$ and $c,\\tilde{h}$ be two admissible pairs of central charge and highest weight for ${\\rm Diff}^+(S^1)$. It is shown here that the positive energy irreducible projective unitary representations $U_{c,h}$ and $U_{c,\\tilde{h}}$ of the group ${\\rm Diff}^+(S^1)$ are locally equivalent. This means that for any $I\\Subset S^1$ open proper interval, there exists a unitary operator $W_I$ such that $W_I U_{c,h}(\\gamma)W_I^* = U_{c,\\tilde{h}}(\\gamma)$ for all $\\gamma \\in {\\rm Diff}^+(S^1)$ which act identically on $I^c\\equiv S^1\\setminus I$ (i.e. which can \"displace\" or \"move\" points only in $I$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00344","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"}