Hamiltonian reduction and nearby cycles for mirabolic D-modules
Hamiltonian reduction and nearby cycles for mirabolic D-modules
复制标题
蜃景 D 模块的哈密尔顿还原和附近循环
DOI：
10.1016/j.aim.2014.10.002
复制
发表时间：
2015-01-10
影响因子：
1.7
通讯作者：
Ginzburg, Victor
中科院分区：
文献类型：
--
作者：
Bellamy, Gwyn;Ginzburg, Victor
我们研究了SLn(C)x C-n上的完整D-模，我们称之为Mirabolic模，类似于Lusztig的特征线。我们描述了简单Mirabolic模的支承。证明了三角Cherednik代数的表示范畴的哈密尔顿约化函子杀死了Mirabolic模当且仅当模的特征簇包含在不稳定的轨迹中.我们引入了一种Verdier的表示Cherednik代数的特化函子的类似形式，它在范畴O上与Bezrukavnikov和Etingof的限制函子一致.在A类中，我们还考虑了Mirabolic D-模上的Verdier专化函子。我们证明了哈密顿约化使Mirabolic D-模上的专门化函子与Cherednik代数表示上的对应函子缠绕在一起。这允许我们在Bezrukavnikov和Etingof所考虑的设置下，将已知的Hodge理论纯度结果应用于附近的周期。(C)2014 Elsevier Inc.保留所有权利。
We study holonomic D-modules on SLn(C) x C-n, called mirabolic modules, analogous to Lusztig's character sheaves. We describe the supports of simple mirabolic modules. We show that a mirabolic module is killed by the functor of Hamiltonian reduction from the category of mirabolic modules to the category of representations of the trigonometric Cherednik algebra if and only if the characteristic variety of the module is contained in the unstable locus.We introduce an analogue of Verdier's specialization functor for representations of Cherednik algebras which agrees, on category O, with the restriction functor of Bezrukavnikov and Etingof. In type A, we also consider a Verdier specialization functor on mirabolic D-modules. We show that Hamiltonian reduction intertwines specialization functors on mirabolic D-modules with the corresponding functors on representations of the Cherednik algebra. This allows us to apply known Hodge-theoretic purity results for nearby cycles in the setting considered by Bezrukavnikov and Etingof. (C) 2014 Elsevier Inc. All rights reserved.