{"paper":{"title":"On modules arising from quantum groups at $p^r$-th roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hankyung Ko","submitted_at":"2016-06-27T19:51:34Z","abstract_excerpt":"This paper studies the \"reduction mod $p$\" method, which constructs large classes of representations for a semisimple algebraic group $G$ from representations for the corresponding Lusztig quantum group $U_\\zeta$ at a $p^r$-th root of unity. The $G$-modules arising in this way include the Weyl modules, the induced modules, and various reduced versions of these modules. We present a relation between $\\operatorname{Ext}^n_G(V,W)$ and $\\operatorname{Ext}^n_{U_\\zeta}(V',W')$, when $V,W$ are obtained from $V',W'$ by reduction mod $p$. Since the dimensions of $\\operatorname{Ext}^n$-spaces for $U_\\ze"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08426","kind":"arxiv","version":2},"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"}