论文标题
小晶体的主管过滤和重量晶格中的路径
Kostant principal filtration and paths in weight lattices
论文作者
论文摘要
一个复杂的简单谎言代数来自截然不同的环境中有几个有趣的过滤：一种是来自兰兰兹双重的主要过滤，一个是来自clifford代数的主要过滤。 Harish-Chandra预测。现在众所周知，所有这些过滤都是一致的。这是由几位作者（Rohr，Joseph，Alekseev和第二名命名作者）的作品组合而成的，并且基本上是由Kostant猜想的。在本文中，我们建立了包围过滤的直接对应关系和A型或C型的简单代数的对称过滤之间的对应关系。我们的证明与Rohr和Joseph的方法大不相同。这个想法是在标准表示的晶体图中使用组合对象（称为加权路径）的对称和包裹不变的显式描述。
There are several interesting filtrations on the Cartan subalgebra of a complex simple Lie algebra coming from very different contexts: one is the principal filtration coming from the Langlands dual, one is coming from the Clifford algebra associated with a non-degenerate invariant bilinear form, one is coming from the symmetric algebra and the Chevalley projection, and two other ones are coming from the enveloping algebra and Harish-Chandra projections. It is now known that all these filtrations coincide. This results from a combination of works of several authors (Rohr, Joseph, Alekseev and the second named author), and was essentially conjectured by Kostant. In this paper, we establish a direct correspondence between the enveloping filtration and the symmetric filtration for a simple Lie algebra of type A or C. Our proof is very different from Rohr and Joseph approaches. The idea is to use an explicit description of the symmetric and enveloping invariants in term of combinatorial objects, called weighted paths, in the crystal graph of the standard representation.
