{"paper":{"title":"B-orbits in abelian nilradicals of types B, C and D: towards a conjecture of Panyushev","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anna Melnikov, Nurit Barnea","submitted_at":"2016-01-12T05:24:33Z","abstract_excerpt":"Let $B$ be a Borel subgroup of a semisimple algebraic group $G$ and let $\\mathfrak m$ be an abelian nilradical in $\\mathfrak b={\\rm Lie} (B)$. Using subsets of strongly orthogonal roots in the subset of positive roots corresponding to $\\mathfrak m$, D. Panyushev \\cite{Pan} gives in particular classification of $B-$orbits in $\\mathfrak m$ and ${\\mathfrak m}^*$ and states general conjectures on the closure and dimensions of the $B-$orbits in both $\\mathfrak m$ and ${\\mathfrak m}^*$ in terms of involutions of the Weyl group. Using Pyasetskii correspondence between $B-$orbits in $\\mathfrak m$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02731","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"}