论文标题
张量产物和几何萨克对应的基础
Bases of tensor products and geometric Satake correspondence
论文作者
论文摘要
几何萨克对应关系可以被视为一个复杂连接的还原群G的几何结构。在对这种对应关系的研究中，Mirković和Vilonen引入了代数周期，在每个不可征象的表示中都提供了线性的基础。贡献者和沉概括了这种结构，在不可减至表示的每种张量产物中定义了线性基础。我们研究了这些基础，并表明它们与Lusztig的双重规范基础共享许多属性。
The geometric Satake correspondence can be regarded as a geometric construction of the rational representations of a complex connected reductive group G. In their study of this correspondence, Mirković and Vilonen introduced algebraic cycles that provide a linear basis in each irreducible representation. Generalizing this construction, Goncharov and Shen define a linear basis in each tensor product of irreducible representations. We investigate these bases and show that they share many properties with the dual canonical bases of Lusztig.
