{"paper":{"title":"On the $T$-leaves and the ranks of a Poisson structure on twisted conjugacy classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.RT","authors_text":"Jiang-Hua Lu","submitted_at":"2016-01-01T04:57:13Z","abstract_excerpt":"Let $G$ be a connected complex semisimple Lie group with a fixed maximal torus $T$ and a Borel subgroup $B \\supset T$. For an arbitrary automorphism $\\theta$ of $G$, we introduce a holomorphic Poisson structure $\\pi_\\theta$ on $G$ which is invariant under the $\\theta$-twisted conjugation by $T$ and has the property that every $\\theta$-twisted conjugacy class of $G$ is a Poisson subvariety with respect to $\\pi_\\theta$. We describe the $T$-orbits of symplectic leaves, called $T$-leaves, of $\\pi_\\theta$ and compute the dimensions of the symplectic leaves (i.e, the ranks) of $\\pi_\\theta$. We give "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00051","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"}