{"paper":{"title":"Lowest degree invariant 2nd order PDEs over rational homogeneous contact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"Dmitri V. Alekseevsky, Gianni Manno, Giovanni Moreno, Jan Gutt","submitted_at":"2016-06-08T16:48:18Z","abstract_excerpt":"For each simple Lie algebra $\\mathfrak{g}$ (excluding, for trivial reasons, type ${\\sf C}$) we find the lowest possible degree of an invariant second-order PDE over the adjoint variety in $\\mathbb{P}\\mathfrak{g}$, a homogeneous contact manifold. Here a PDE $F(x^i,u,u_i,u_{ij})=0$ has degree $\\le d$ if $F$ is a polynomial of degree $\\le d$ in the minors of $(u_{ij})$, with coefficients functions of the contact coordinates $x^i$, $u$, $u_i$ (e.g., Monge-Amp\\`ere equations have degree 1). For $\\mathfrak{g}$ of type ${\\sf A}$ or ${\\sf G}$ we show that this gives all invariant second-order PDEs. Fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02633","kind":"arxiv","version":3},"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"}