{"paper":{"title":"Highest Weights for Categorical Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"David Ben-Zvi, Hendrik Orem, Sam Gunningham","submitted_at":"2016-08-29T22:30:27Z","abstract_excerpt":"We present a criterion for establishing Morita equivalence of monoidal categories, and apply it to the categorical representation theory of reductive groups $G$. We show that the \"de Rham group algebra\" $\\mathcal D(G)$ (the monoidal category of $\\mathcal D$-modules on $G$) is Morita equivalent to the universal Hecke category $\\mathcal D(N \\backslash G/N)$ and to its monodromic variant $\\widetilde{\\mathcal D}(B \\backslash G / B)$. In other words, de Rham $G$-categories, i.e., module categories for $\\mathcal D(G)$, satisfy a \"highest weight theorem\" - they all appear in the decomposition of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08273","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"}