{"paper":{"title":"Generalized adjoint actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Arkady Berenstein, Vladimir Retakh","submitted_at":"2015-06-23T16:10:04Z","abstract_excerpt":"The aim of this paper is to generalize the classical formula $e^xye^{-x}=\\sum\\limits_{k\\ge 0} \\frac{1}{k!} (ad~x)^k(y)$ by replacing $e^x$ with any formal power series $\\displaystyle {f(x)=1+\\sum_{k\\ge 1} a_kx^k}$. We also obtain combinatorial applications to $q$-exponentials, $q$-binomials, and Hall-Littlewood polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07071","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"}