{"paper":{"title":"The symmetric invariants of centralizers and Slodowy grading II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anne Moreau, Jean-Yves Charbonnel","submitted_at":"2016-04-05T14:34:59Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a finite-dimensional simple Lie algebra of rank $\\ell$ over an algebraically closed field $\\Bbbk$ of characteristic zero, and let $(e,h,f)$ be an $\\mathfrak{sl}_2$-triple of g. Denote by $\\mathfrak{g}^{e}$ the centralizer of $e$ in $\\mathfrak{g}$ and by ${\\rm S}(\\mathfrak{g}^{e})^{\\mathfrak{g}^{e}}$ the algebra of symmetric invariants of $\\mathfrak{g}^{e}$. We say that $e$ is good if the nullvariety of some $\\ell$ homogenous elements of ${\\rm S}(\\mathfrak{g}^{e})^{\\mathfrak{g}^{e}}$ in $(\\mathfrak{g}^{e})^{*}$ has codimension $\\ell$. If $e$ is good then ${\\rm S}(\\mathfrak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01274","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":""},"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"}