{"paper":{"title":"Integral $u$-deformed involution modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jun Hu, Yujiao Sun","submitted_at":"2018-12-11T06:27:42Z","abstract_excerpt":"Let $(W,S)$ be a Coxeter system and $\\ast$ an automorphism of $W$ with order $\\leq 2$ and $S^{\\ast}=S$. Lusztig and Vogan ([11], [14]) have introduced a $u$-deformed version $M_u$ of Kottwitz's involution module over the Iwahori-Hecke algebra $\\mathscr{H}_{u}(W)$ with Hecke parameter $u^2$, where $u$ is an indeterminate. Lusztig has proved that $M_u$ is isomorphic to the left $\\mathscr{H}_{u}(W)$-submodule of ${\\hat{\\mathscr{H}}}_u$ generated by $X_{\\emptyset}:=\\sum_{w^*=w\\in W}{u^{-\\ell(w)}T_w}$, where ${\\hat{\\mathscr{H}}}_u$ is the vector space consisting of all formal (possibly infinite) su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04231","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"}