{"paper":{"title":"Cohomology in singular blocks for a quantum group at a root of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Hankyung Ko","submitted_at":"2016-05-15T14:31:08Z","abstract_excerpt":"Let $U_\\zeta$ be a Lusztig quantum enveloping algebra associated to a complex semisimple Lie algebra $\\mathfrak g$ and a root of unity $\\zeta$. When $L,L'$ are irreducible $U_\\zeta$-modules having regular highest weights, the dimension of $\\operatorname{Ext}^n_{U_\\zeta}(L,L')$ can be calculated in terms of the coefficients of appropriate Kazhdan-Lusztig polynomials associated to the affine Weyl group of $U_\\zeta$. This paper shows for $L,L'$ irreducible modules in a singular block that $\\dim\\operatorname{Ext}^n_{U_\\zeta}(L,L')$ is explicitly determined using the coefficients of parabolic Kazhd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04556","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"}