{"paper":{"title":"On cellularity of Hecke Algebras for Wreath Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Berta Hudak, Chun-Ju Lai","submitted_at":"2026-06-02T15:15:16Z","abstract_excerpt":"The (generalized) Hu algebra is a nontrivial quantization of the wreath product $\\Sigma_m \\wr \\Sigma_d$ between symmetric groups, whose representation theory controls the Hecke algebra of the complex reflection group $G(d,d,md)$. In this paper, we construct a unified basis for this algebra and establish its cellular algebra structure in the case $d = 2$. As an application, our construction provides an elementary realization of the simple modules for the Hecke algebra of type $D_{2m}$ that are parameterized by bipartitions of size $(m,m)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03759","kind":"arxiv","version":1},"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/2606.03759/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"}