{"paper":{"title":"Differential operators on quantized flag manifolds at roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Toshiyuki Tanisaki","submitted_at":"2010-01-31T07:53:39Z","abstract_excerpt":"The quantized flag manifold, which is a $q$-analogue of the ordinary flag manifold, is realized as a non-commutative scheme, and we can define the category of $D$-modules on it using the framework of non-commutative algebraic geometry; however, when the parameter $q$ is a root of unity, Lusztig's Frobenius morphism allows us to handle $D$-modules on the quantized flag manifold through modules over a certain sheaf of rings on the ordinary flag manifold. In this paper we will show that this sheaf of rings on the ordinary flag manifold is an Azumaya algebra over its center. We also show that its "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0113","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"}