{"paper":{"title":"Restricted shifted Yangians and restricted finite $W$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Lewis Topley, Simon M. Goodwin","submitted_at":"2019-03-07T18:10:59Z","abstract_excerpt":"We study the truncated shifted Yangian $Y_{n,l}(\\sigma)$ over an algebraically closed field $\\mathbb{k}$ of characteristic $p > 0$, which is known to be isomorphic to the finite $W$-algebra $U(\\mathfrak{g}, e)$ associated to a corresponding nilpotent element $e\\in \\mathfrak{g} = \\mathfrak{gl}_N(\\mathbb{k})$. We obtain an explicit description of the centre of $Y_{n,l}(\\sigma)$, showing that it is generated by its Harish-Chandra centre and its $p$-centre. We define $Y_{n,l}^{[p]}(\\sigma)$ to be the quotient of $Y_{n,l}(\\sigma)$ by the ideal generated by the kernel of trivial character of its $p$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03079","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"}