{"paper":{"title":"Properties of non-symmetric Macdonald polynomials at $q=1$ and $q=0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Mehtaab Sawhney, Per Alexandersson","submitted_at":"2018-01-14T13:01:55Z","abstract_excerpt":"We examine the non-symmetric Macdonald polynomials $E_\\lambda(x;q,t)$ at $q=1$, as well as the more general permuted-basement Macdonald polynomials. When $q=1$, we show that $E_\\lambda(x;1,t)$ is symmetric and independent of $t$ whenever $\\lambda$ is a partition. Furthermore, we show that for general $\\lambda$, this expression factors into a symmetric and a non-symmetric part, where the symmetric part is independent of $t$, while the non-symmetric part only depends on the relative order of the entries in $\\lambda$.\n  We also examine the case $q=0$, which give rise to so called permuted-basemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04550","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"}