{"paper":{"title":"Symmetric structure for the endomorphism algebra of projective-injective module in parabolic category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jun Hu, Ngau Lam","submitted_at":"2017-02-20T02:10:24Z","abstract_excerpt":"We show that for any singular dominant integral weight $\\lambda$ of a complex semisimple Lie algebra $\\mathfrak{g}$, the endomorphism algebra $B$ of any projective-injective module of the parabolic BGG category $\\mathcal{O}_\\lambda^{\\mathfrak{p}}$ is a symmetric algebra (as conjectured by Khovanov) extending the results of Mazorchuk and Stroppel for the regular dominant integral weight. Moreover, the endomorphism algebra $B$ is equipped with a homogeneous (non-degenerate) symmetrizing form. In the appendix, there is a short proof due to K. Coulembier and V. Mazorchuk showing that the endomorph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05834","kind":"arxiv","version":4},"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"}