{"paper":{"title":"B-orbits of square zero in nilradical of the symplectic algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anna Melnikov, Nurit Barnea","submitted_at":"2015-09-20T12:48:21Z","abstract_excerpt":"Let $SP_n(\\mathbb{C})$ be the symplectic group and $\\mathfrak{sp}_n(\\mathbb{C})$ its Lie algebra. Let $B$ be a Borel subgroup of $SP_n(\\mathbb{C} )$, $\\mathfrak{b}={\\rm Lie}(B)$ and $\\mathfrak n$ its nilradical. Let $\\mathcal X$ be a subvariety of elements of square 0 in $\\mathfrak n.$ $B$ acts adjointly on $\\mathcal X$. In this paper we describe topology of orbits $\\mathcal X/B$ in terms of symmetric link patterns.\n  Further we apply this description to the computations of the closures of orbital varieties of nilpotency order 2 and to their intersections. In particular we show that all the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06008","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"}