{"paper":{"title":"Enright resolutions encoded by a generating function for Blattner's formula: Type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"William Q. Erickson","submitted_at":"2021-08-19T03:25:46Z","abstract_excerpt":"Consider the classical action of ${\\rm GL}_n$ on a sum of $q$ copies of the defining representation and $p$ copies of its dual; by Howe duality, the polynomial functions on this space decompose under the joint action of ${\\rm GL}_n$ and $\\mathfrak{gl}_{p+q}$. The modules for $\\mathfrak{gl}_{p+q}$ are infinite-dimensional and their structure is complicated outside a certain stable range, although Enright and Willenbring (2005) constructed resolutions in terms of generalized Verma modules. We show that these resolutions can be read off from the coefficients in a formal series arising in an entir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.08469","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.08469/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}