{"paper":{"title":"The relation between Parabolic Hecke modules and $W$-graph ideal modules in Kazhdan-Lusztig theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qi Wang","submitted_at":"2018-05-02T01:51:03Z","abstract_excerpt":"In 2011, Howlett and Nguyen \\cite{r1} introduced the concept of a $W$-graph ideal $E_J$ in $\\left ( W,\\leqslant_{L} \\right )$ with respect to $J$ (a subset of $S$), where $\\leqslant _{L}$ is the left weak order on $W$. They proved that one can construct a $W$-graph from a given $W$-graph ideal by constructing a Hecke module structure on $E_J$, where the $W$-graph was introduced by Kazhdan and Lusztig in \\cite{d1}.\n  In this paper, we give the relation between Hecke modules on $E_J$ and general Hecke algebras by considering the relation between Hecke modules on $E_J$ and parabolic Hecke modules"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00598","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":""},"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"}