{"paper":{"title":"The based ring the lowest generalized two-sided cell of an extended affine Weyl group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Xun Xie","submitted_at":"2014-03-13T09:38:04Z","abstract_excerpt":"Let $\\mathbf{c}_0$ be the lowest generalized two-sided cell of an extended affine Weyl group W. We determine the structure of the based ring of $\\mathbf{c}_0$. For this we show that certain conjectures of Lusztig on generalized cells (called P1-P15) hold for $\\mathbf{c}_0$. As an application, we use the structure of the based ring to study certain simple modules of Hecke algebras of $ W $ with unequal parameters, namely those attached to $\\mathbf{c}_0$.\n  Also we give a set of prime ideals $\\mathfrak{p}$ of the center $\\mathcal{Z}$ of the generic affine Hecke algebra $\\mathcal{H}$ such that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3213","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"}