Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups
Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups
复制标题
某些反射群的等变相干滑轮类别的半正交分解
DOI：
10.4171/jems/890
复制
发表时间：
2015
影响因子：
2.6
通讯作者：
M. Bergh
中科院分区：
文献类型：
--
作者：
A. Polishchuk;M. Bergh
我们考虑复向量空间上相干层的导出范畴关于有限反射群G的作用等变。在某些情形下，包括A，B，G_2，F_4型Weyl群，以及群G（m，1，n），我们构造了这个范畴的一个半正交分解，它以G的共轭类为指标.这种分解的片段等价于一致空间V^g/C（g）上的凝聚层的导出范畴，其中C（g）是g在G中的中心化子子群。在外尔群的情况下，建设使用一些关键的结果，斯普林格对应，由于卢斯蒂格，沿着一些形式的声明，推广了结果德利涅。我们还构造了一些半正交分解的全局类似物，这些半正交分解涉及C^n上的等变相干层的导出范畴，其中C是光滑曲线。
We consider the derived category of coherent sheaves on a complex vector space equivariant with respect to an action of a finite reflection group G. In some cases, including Weyl groups of type A, B, G_2, F_4, as well as the groups G(m,1,n), we construct a semiorthogonal decomposition of this category, indexed by the conjugacy classes of G. The pieces of this decompositions are equivalent to the derived categories of coherent sheaves on the quotient-spaces V^g/C(g), where C(g) is the centralizer subgroup of g in G. In the case of the Weyl groups the construction uses some key results about the Springer correspondence, due to Lusztig, along with some formality statement generalizing a result of Deligne. We also construct global analogs of some of these semiorthogonal decompositions involving derived categories of equivariant coherent sheaves on C^n, where C is a smooth curve.