{"paper":{"title":"On a theorem of Lehrer and Zhang","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jun Hu, Zhankui Xiao","submitted_at":"2011-05-26T13:45:47Z","abstract_excerpt":"Let $K$ be an arbitrary field of characteristic not equal to 2. Let $m, n\\in\\N$ and $V$ an $m$ dimensional orthogonal space over $K$. There is a right action of the Brauer algebra $\\bb_n(m)$ on the $n$-tensor space $V^{\\otimes n}$ which centralizes the left action of the orthogonal group $O(V)$. Recently G.I. Lehrer and R.B. Zhang defined certain quasi-idempotents $E_i$ in $\\bb_n(m)$ (see (\\ref{keydfn})) and proved that the annihilator of $V^{\\otimes n}$ in $\\bb_n(m)$ is always equal to the two-sided ideal generated by $E_{[(m+1)/2]}$ if $\\ch K=0$ or $\\ch K>2(m+1)$. In this paper we extend thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5287","kind":"arxiv","version":3},"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"}