{"paper":{"title":"Action of special linear groups to the tensor of indeterminates, classical invariants of binary forms and hyperdeterminant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mitsuhiro Miyazaki","submitted_at":"2013-01-29T16:49:47Z","abstract_excerpt":"In this paper, we study the ring of invariants under the action of SL(m,K)\\times SL(n,K) and SL(m,K)\\times SL(n,K)\\times SL(2,K) on the 3-dimensional array of indeterminates of form m\\times n\\times 2, where K is an infinite field. And we show that if m=n\\geq 2, then the ring of SL(n,K)\\times SL(n,K)-invariants is generated by n+1 algebraically independent elements over K and the action of SL(2,K) on that ring is identical with the one defined in the classical invariant theory of binary forms. We also reveal the ring of SL(m,K)\\times SL(n,K)-invariants and SL(m,K)\\times SL(n,K)\\times SL(2,K)-in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6979","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"}