{"paper":{"title":"Some complete intersection symplectic quotients in positive characteristic: invariants of a vector and a covector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"C\\'edric Bonnaf\\'e (LM-Besan\\c{c}on), G. Kemper","submitted_at":"2010-06-24T11:55:11Z","abstract_excerpt":"Given a linear action of a group $G$ on a $K$-vector space $V$, we consider the invariant ring $K[V \\oplus V^*]^G$, where $V^*$ is the dual space. We are particularly interested in the case where $V =\\gfq^n$ and $G$ is the group $U_n$ of all upper unipotent matrices or the group $B_n$ of all upper triangular matrices in $\\GL_n(\\gfq)$. In fact, we determine $\\gfq[V \\oplus V^*]^G$ for $G = U_n$ and $G =B_n$. The result is a complete intersection for all values of $n$ and $q$. We present explicit lists of generating invariants and their relations. This makes an addition to the rather short list o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4762","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"}