{"paper":{"title":"Stokes phenomenon, Gelfand-Zeitlin systems and relative Ginzburg-Weinstein linearization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","math.SG"],"primary_cat":"math-ph","authors_text":"Xiaomeng Xu","submitted_at":"2017-01-27T16:54:27Z","abstract_excerpt":"In 2007, Alekseev-Meinrenken proved that there exists a Ginzburg-Weinstein diffeomorphism from the dual Lie algebra ${\\rm u}(n)^*$ to the dual Poisson Lie group $U(n)^*$ compatible with the Gelfand-Zeitlin integrable systems. In this paper, we explicitly construct such diffeomorphisms via Stokes phenomenon and Boalch's dual exponential maps. Then we introduce a relative version of the Ginzburg-Weinstein linearization motivated by irregular Riemann-Hilbert correspondence, and generalize the results of Enriquez-Etingof-Marshall to this relative setting. In particular, we prove the connection mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08113","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"}