{"paper":{"title":"Admissible subsets and Littelmann paths in affine Kazhdan-Lusztig theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Jeremie Guilhot","submitted_at":"2016-06-17T14:48:39Z","abstract_excerpt":"The center of an extended affine Hecke algebra is known to be isomorphic to the ring of symmetric functions associated to the underlying finite Weyl group $W\\_0$. The set of Weyl characters ${\\sf s}\\_\\la$ forms a basis of the center and Lusztig showed in [Lus15] that these characters act as translations on the Kazhdan-Lusztig basis element $C\\_{w\\_0}$ where $w\\_0$ is the longest element of $W\\_0$, that is we have $C\\_{w\\_0}{\\sf s}\\_\\la =C\\_{w\\_0t\\_\\la}$. As a consequence, the coefficients that appear when decomposing~$C\\_{w\\_0t\\_{\\la}}{\\sf s}\\_\\tau$ in the Kazhdan-Lusztig basis are tensor mult"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05542","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"}