{"paper":{"title":"Bott-Samelson varieties and Poisson Ore extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"Balazs Elek, Jiang-Hua Lu","submitted_at":"2016-01-01T04:31:05Z","abstract_excerpt":"Let $G$ be a connected complex semi-simple Lie group, and let $Z_{{\\bf u}}$ be an $n$-dimensional Bott-Samelson variety of $G$, where ${\\bf u}$ is any sequence of simple reflections in the Weyl group of $G$. We study the Poisson structure $\\pi_n$ on $Z_{\\bf u}$ defined by a standard multiplicative Poisson structure $\\pi_{\\rm st}$ on $G$. We explicitly express $\\pi_n$ on each of the $2^n$ affine coordinate charts, one for every subexpression of ${\\bf u}$, in terms of the root strings and the structure constants of the Lie algebra of $G$. We show that the restriction of $\\pi_n$ to each affine co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00047","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"}