Quantized multiplicative quiver varieties
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- 作者：David Jordan
- 关键词：Quiver variety ; Hamiltonian reduction ; Moment map ; q-Deformation ; Double affine Hecke algebra ; Differential operators
- 刊名：Advances in Mathematics
- 出版年：15 January, 2014
- 年：2014
- 卷：250
- 期：Complete
- 页码：420-466
- 全文大小：465 K
文摘
Beginning with the data of a quiver Q, and its dimension vector d, we construct an algebra , which is a flat q-deformation of the algebra of differential operators on the affine space . The algebra is equivariant for an action by a product of quantum general linear groups, acting by conjugation at each vertex. We construct a quantum moment map for this action, and subsequently define the Hamiltonian reduction of with moment parameter 位. We show that is a flat formal deformation of Lusztig始s quiver varieties, and their multiplicative counterparts, for all dimension vectors satisfying a flatness condition of Crawley-Boevey: indeed the product on yields a Fedosov quantization the of symplectic structure on multiplicative quiver varieties. As an application, we give a description of the category of representations of the spherical double affine Hecke algebra of type , and its generalization constructed by Etingof, Oblomkov, and Rains, in terms of a quotient of the category of equivariant -modules by a Serre subcategory of aspherical modules.