{"paper":{"title":"Whittaker coinvariants for $\\mathrm{GL}(m|n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Jonathan Brundan, Simon M. Goodwin","submitted_at":"2016-12-24T08:08:17Z","abstract_excerpt":"Let $W_{m|n}$ be the (finite) $W$-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra $\\mathfrak{gl}_{m|n}(\\mathbb{C})$. In this paper we study the {\\em Whittaker coinvariants functor}, which is an exact functor from category $\\mathcal O$ for $\\mathfrak{gl}_{m|n}(\\mathbb{C})$ to a certain category of finite-dimensional modules over $W_{m|n}$. We show that this functor has properties similar to Soergel's functor $\\mathbb V$ in the setting of category $\\mathcal O$ for a semisimple Lie algebra. We also use it to compute the center of $W_{m|n}$ explicitly, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08152","kind":"arxiv","version":3},"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"}