{"paper":{"title":"A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Jacob Greenstein, Vyjayanthi Chari","submitted_at":"2008-08-11T08:22:55Z","abstract_excerpt":"Let $\\lie g$ be a simple Lie algebra and let $\\bs^{\\lie g}$ be the locally finite part of the algebra of invariants $(_\\bc\\bv\\otimes S(\\lie g))^{\\lie g}$ where $\\bv$ is the direct sum of all simple finite-dimensional modules for $\\lie g$ and $S(\\lie g)$ is the symmetric algebra of $\\lie g$. Given an integral weight $\\xi$, let $\\Psi=\\Psi(\\xi)$ be the subset of roots which have maximal scalar product with $\\xi$. Given a dominant integral weight $\\lambda$ and $\\xi$ such that $\\Psi$ is a subset of the positive roots we construct a finite-dimensional subalgebra $\\bs^{\\lie g}_\\Psi(\\le_\\Psi\\lambda)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1463","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"}