{"paper":{"title":"${\\rm SL}(m,C)$-equivariant and translation covariant continuous tensor valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"D\\'avid Kert\\'esz, Judit Abardia-Ev\\'equoz, K\\'aroly J. B\\\"or\\\"oczky, M\\'aty\\'as Domokos","submitted_at":"2018-01-26T05:47:52Z","abstract_excerpt":"The space of continuous, ${\\rm SL}(m,C)$-equivariant, $m\\geq 2$, and translation covariant valuations taking values in the space of real symmetric tensors on $C^m\\cong R^{2m}$ of rank $r\\geq 0$ is completely described. The classification involves the moment tensor valuation for $r\\geq 1$ and is analogous to the classification of the corresponding tensor valuations that are ${\\rm SL}(2m,R)$-equivariant, although the method of proof cannot be adapted."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08680","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"}