Poisson Traces for Symmetric Powers of Symplectic Varieties
Poisson Traces for Symmetric Powers of Symplectic Varieties
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DOI：
10.1093/imrn/rnt031
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发表时间：
2014-01-01
影响因子：
1
通讯作者：
Schedler, Travis
中科院分区：
文献类型：
--
作者：
Etingof, Pavel;Schedler, Travis
我们计算仿射辛簇对称幂上的泊松迹空间。在辛向量空间的情况下，我们还考虑对角平移作用的商，其中包括与 AWeyl 群 Sn 类型及其反射表示 Cn-1 相关的商奇点 T* Cn-1/Sn。我们还计算了作者之前定义的自然 D 模的完整结构，其代数分布的解空间与泊松迹空间一致。因此，我们推导出有限维不可约表示的数量界限以及这些簇的量化的素理想。最后，受这些结果的启发，我们提出了辛分辨率的猜想，并给出了自然 D 模的相关例子。在附录中，第二作者计算了与 D 型 Weyl 群关联的商 T* Cn/Dn 的泊松迹和关联的 D 模。在第二个附录中，同一作者提供了主要定理之一的直接证明。
We compute the space of Poisson traces on symmetric powers of affine symplectic varieties. In the case of symplectic vector spaces, we also consider the quotient by the diagonal translation action, which includes the quotient singularities T* Cn-1/Sn associated with the type AWeyl group Sn and its reflection representation Cn-1. We also compute the full structure of the natural D-module, previously defined by the authors, whose solution space over algebraic distributions identifies with the space of Poisson traces. As a consequence, we deduce bounds on the numbers of finite-dimensional irreducible representations and prime ideals of quantizations of these varieties. Finally, motivated by these results, we pose conjectures on symplectic resolutions, and give related examples of the natural D-module. In an appendix, the second author computes the Poisson traces and associated D-module for the quotients T* Cn/Dn associated with type D Weyl groups. In a second appendix, the same author provides a direct proof of one of the main theorems.