{"paper":{"title":"q-Whittaker functions, finite fields, and Jordan forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.RT"],"primary_cat":"math.CO","authors_text":"Hugh Thomas, Steven N. Karp","submitted_at":"2022-07-26T00:53:43Z","abstract_excerpt":"The $q$-Whittaker function $W_\\lambda(\\mathbf{x};q)$ associated to a partition $\\lambda$ is a $q$-analogue of the Schur function $s_\\lambda(\\mathbf{x})$, and is defined as the $t=0$ specialization of the Macdonald polynomial $P_\\lambda(\\mathbf{x};q,t)$. We show combinatorially how to expand $W_\\lambda(\\mathbf{x};q)$ in terms of partial flags compatible with a nilpotent endomorphism over the finite field of size $1/q$. This yields an expression analogous to a well-known formula for the Hall-Littlewood functions. We show that considering pairs of partial flags and taking Jordan forms leads to a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12590","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.12590/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}