{"paper":{"title":"On invariant fields of vectors and covectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David L. Wehlau, Yin Chen","submitted_at":"2017-08-04T17:23:44Z","abstract_excerpt":"Let ${\\mathbb{F}_{q}}$ be the finite field of order $q$. Let $G$ be one of the three groups ${\\rm GL}(n, \\mathbb{F}_q)$, ${\\rm SL}(n, \\mathbb{F}_q)$ or ${\\rm U}(n, \\mathbb{F}_q)$ and let $W$ be the standard $n$-dimensional representation of $G$. For non-negative integers $m$ and $d$ we let $mW\\oplus d W^*$ denote the representation of $G$ given by the direct sum of $m$ vectors and $d$ covectors. We exhibit a minimal set of homogenous invariant polynomials $\\{\\ell_1,\\ell_{2},\\dots,\\ell_{(m+d)n}\\}\\subseteq \\mathbb{F}_q[mW\\oplus d W^*]^G$ such that $\\mathbb{F}_q(mW\\oplus d W^*)^G=\\mathbb{F}_q(\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01593","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"}