{"paper":{"title":"Deligne categories and representations of the finite general linear group, part 1: universal property","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Inna Entova-Aizenbud, Thorsten Heidersdorf","submitted_at":"2022-07-30T14:51:58Z","abstract_excerpt":"We study the Deligne interpolation categories $\\underline{\\mathrm{Rep}}(GL_{t}(\\mathbb{F}_q))$ for $t\\in \\mathbb{C}$, first introduced by F. Knop. These categories interpolate the categories of finite dimensional complex representations of the finite general linear group $GL_n(\\mathbb{F}_q)$. We describe the morphism spaces in this category via generators and relations. We show that the generating object of this category (an analogue of the representation $\\mathbb{C}\\mathbb{F}_q^n$ of $GL_n(\\mathbb{F}_q)$) carries the structure of a Frobenius algebra with a compatible $\\mathbb{F}_q$-linear str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.00241","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.00241/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"}