{"paper":{"title":"Molien series and low-degree invariants for a natural action of ${\\bf SO}(3)\\wr{\\bf Z}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"David Chillingworth, Reiner Lauterbach, Stefano Turzi","submitted_at":"2014-07-24T21:19:55Z","abstract_excerpt":"We investigate the invariants of the $25$-dimensional real representation of the group ${\\bf SO}(3)\\wr{\\bf Z}_2$ given by the left and right actions of ${\\bf SO}(3)$ on $5\\times 5$ matrices together with matrix transposition; the action on column vectors is the irreducible $5$-dimensional representation of ${\\bf SO}(3)$. The $25$-dimensional representation arises naturally in the study of nematic liquid crystals, where the second-rank orientational order parameters of a molecule are represented by a symmetric $3\\times3$ traceless symmetric matrix, and where a rigid rotation in ${\\bf R}^3$ indu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6738","kind":"arxiv","version":1},"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"}