{"paper":{"title":"Hall-Littlewood polynomials and a Hecke action on ordered set partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, Jia Huang, Travis Scrimshaw","submitted_at":"2017-09-23T03:34:50Z","abstract_excerpt":"We construct an action of the Hecke algebra $H_n(q)$ on a quotient of the polynomial ring $F[x_1, \\dots, x_n]$, where $F = \\mathbb{Q}(q)$. The dimension of our quotient ring is the number of $k$-block ordered set partitions of $\\{1, 2, \\dots, n \\}$. This gives a quantum analog of a construction of Haglund-Rhoades-Shimozono and interpolates between their result at $q = 1$ and work of Huang-Rhoades at $q = 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07995","kind":"arxiv","version":3},"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"}