{"paper":{"title":"Elliptic Algebra U_{q,p}(g^) and Quantum Z-algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hitoshi Konno, Kazuyuki Oshima, Rasha M. Farghly","submitted_at":"2014-04-07T10:51:50Z","abstract_excerpt":"A new definition of the elliptic algebra U_{q,p}(g^) associated with an untwisted affine Lie algebra g^ is given as a topological algebra over the ring of formal power series in p. We also introduce a quantum dynamical analogue of Lepowsky-Wilson's Z-algebras. The Z-algebra governs the irreducibility of the infinite dimensional U_{q,p}(g^)-modules. Some level-1 examples indicate a direct connection of the irreducible U_{q,p}(g^)-modules to those of the W-algebras associated with the coset g^ \\oplus g^ \\supset (g^)_{diag} with level (r-g-1,1) (g:the dual Coxeter number), which includes Fateev- "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1738","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":""},"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"}