{"paper":{"title":"Double quantization on coadjoint representations of simple Lie groups and its orbits","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"J. Donin","submitted_at":"1999-09-27T15:27:13Z","abstract_excerpt":"Let M be a manifold with an action of a Lie group G, $\\A$ the function algebra on M.\n  The first problem we consider is to construct a $U_h(\\g)$ invariant quantization, $\\A_h$, of $\\A$, where $U_h(\\g)$ is a quantum group corresponding to G.\n  Let s be a G invariant Poisson bracket on M. The second problem we consider is to construct a $U_h(\\g)$ invariant two parameter (double) quantization, $\\A_{t,h}$, of $\\A$ such that $\\A_{t,0}$ is a G invariant quantization of $s$. We call $\\A_{t,h}$ a $U_h(\\g)$ invariant quantization of the Poisson bracket s.\n  In the paper we study the cases when G is a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9909160","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9909160/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}