Dunkl operator and quantization of $\mathbb{Z}_2$-singularity
| Autor: | Halbout, Gilles, Tang, Xiang |
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| Rok vydání: | 2009 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 star-product as a composition of symbol of pseudodifferential operators in the case where partial derivatives are replaced with Dunkl operators. The star-products we obtain can be seen as globalizations of symplectic reflection algebras. Comment: 24 pages |
| Databáze: | arXiv |
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