论文标题
Quaternionic Satake等效性
Quaternionic Satake equivalence
论文作者
论文摘要
我们建立了Quaternionic General Linear gl_n（H）的派生几何萨克等效性。通过应用仿生草植物的实数对应关系，我们获得了对称品种GL_2N/sp_2n的衍生几何萨克等值。我们解释了这些等价如何适合真实群体和相对兰兰兹二元猜想的几何兰兰对应的一般框架。作为应用程序，我们计算了Quaternionic offine Grassmannian和GL_2N/SP_2N的Quaternic offine Grassmannian中的球形轨道闭合的IC复合物的茎。我们显示茎是由GL_N的Kostka-Foulkes多项式给出的，但所有程度都翻了一番。
We establish a derived geometric Satake equivalence for the quaternionic general linear group GL_n(H). By applying the real-symmetric correspondence for affine Grassmannians, we obtain a derived geometric Satake equivalence for the symmetric variety GL_2n/Sp_2n. We explain how these equivalences fit into the general framework of a geometric Langlands correspondence for real groups and the relative Langlands duality conjecture. As an application, we compute the stalks of the IC-complexes for spherical orbit closures in the quaternionic affine Grassmannian and the loop space of GL_2n/Sp_2n. We show the stalks are given by the Kostka-Foulkes polynomials for GL_n but with all degrees doubled.
