{"paper":{"title":"Conjecture $\\mathcal{O}$ holds for the odd symplectic Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Changzheng Li, Leonardo C. Mihalcea, Ryan Shifler","submitted_at":"2017-06-02T16:33:18Z","abstract_excerpt":"Let $\\mathrm{IG}(k, 2n+1)$ be the odd-symplectic Grassmannian. Property $\\mathcal{O}$, introduced by Galkin, Golyshev and Iritani for arbitrary complex, Fano manifolds $X$, is a statement about the eigenvalues of the linear operator obtained by the quantum multiplication by the anticanonical class of $X$. We prove that property $\\mathcal{O}$ holds in the case when $X= \\mathrm{IG}(k, 2n+1)$ is an odd-symplectic Grassmannian. The proof uses the combinatorics of the recently found quantum Chevalley formula for $\\mathrm{IG}(k, 2n+1)$, together with the Perron-Frobenius theory of nonnegative matric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00744","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"}