论文标题
小量子组中心的几何实现
A geometric realization of the center of the small quantum group
论文作者
论文摘要
我们使用某些仿射弹簧纤维的共同体为小量子组中心提出了一个新的几何模型。更确切地说，我们在偏移元件的仿生spaltenstein纤维的仿射纤维同构和小量子组的变形分级模块的中心之间建立了同构。我们还从延伸的仿生基团到兰兰德双重组行动下的小量子群中心不变的部分的行动中，从非公平共同体的不变部分中获得嵌入，我们认为这是同构的。最后，我们给出了共同体方面的不变性尺寸公式，从而为中心的维度提供了下限。
We propose a new geometric model for the center of the small quantum group using the cohomology of certain affine Springer fibers. More precisely, we establish an isomorphism between the equivariant cohomology of affine Spaltenstein fibers for a split element and the center of the deformed graded modules for the small quantum group. We also obtain an embedding from the invariant part of the nonequivariant cohomology under the action of the extended affine Weyl group to the invariant part of the center of the small quantum group under Langlands dual group action, which we conjecture to be an isomorphism. Finally, we give a dimension formula for the invariants on the cohomology side, thus providing a lower bound for the dimension of the center.
