{"paper":{"title":"Dunkl operator and quantization of $\\mathbb{Z}_2$-singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.QA","authors_text":"Gilles Halbout, Xiang Tang","submitted_at":"2009-08-28T22:32:46Z","abstract_excerpt":"Let $(X,\\omega)$ be a symplectic orbifold which is locally like the quotient of a $\\mathbb{Z}_2$ action on $\\reals^n$. Let $A^{((\\hbar))}_X$ be a deformation quantization of $X$ constructed via the standard Fedosov method with characteristic class being $\\omega$. In this paper, we construct a universal deformation of the algebra $A^{((\\hbar))}_X$ parametrized by codimension 2 components of the associated inertia orbifold $\\widetilde{X}$. This partially confirms a conjecture of Dolgushev and Etingof in the case of $\\mathbb{Z}_2$ orbifolds. To do so, we generalize the interpretation of Moyal sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4301","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"}