{"paper":{"title":"Positive Systems of Kostant Roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ivan Dimitrov, Mike Roth","submitted_at":"2016-12-08T21:47:48Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a simple complex Lie algebra and let $\\mathfrak{t} \\subset \\mathfrak{g}$ be a toral subalgebra of $\\mathfrak{g}$. As a $\\mathfrak{t}$-module $\\mathfrak{g}$ decomposes as \\[\\mathfrak{g} = \\mathfrak{s} \\oplus \\big(\\oplus_{\\nu \\in \\mathcal{R}} \\mathfrak{g}^\\nu\\big)\\] where $\\mathfrak{s} \\subset \\mathfrak{g}$ is the reductive part of a parabolic subalgebra of $\\mathfrak{g}$ and $\\mathcal{R}$ is the Kostant root system associated to $\\mathfrak{t}$. When $\\mathfrak{t}$ is a Cartan subalgebra of $\\mathfrak{g}$ the decomposition above is nothing but the root decomposition of $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02851","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"}