{"paper":{"title":"Hall-Littlewood expansions of Schur delta operators at $t = 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, James Haglund, Mark Shimozono","submitted_at":"2018-01-24T15:20:12Z","abstract_excerpt":"For any Schur function $s_{\\nu}$, the associated {\\em delta operator} $\\Delta'_{s_{\\nu}}$ is a linear operator on the ring of symmetric functions which has the modified Macdonald polynomials as an eigenbasis. When $\\nu = (1^{n-1})$ is a column of length $n-1$, the symmetric function $\\Delta'_{e_{n-1}} e_n$ appears in the Shuffle Theorem of Carlsson-Mellit. More generally, when $\\nu = (1^{k-1})$ is any column the polynomial $\\Delta'_{e_{k-1}} e_n$ is the symmetric function side of the Delta Conjecture of Haglund-Remmel-Wilson. We give an expansion of $\\omega \\Delta'_{s_{\\nu}} e_n$ at $t = 0$ in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08017","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"}