论文标题
代表理论的完美基地：三个山脉及其泉水
Perfect bases in representation theory: three mountains and their springs
论文作者
论文摘要
为了给出张量乘积多数群的组合描述，为半imple群提供了与lie代数的Chevalley发电机兼容的表示基础很有用的。这样的基地有三个已知的例子，每个基础都来自几何或代数山。值得注意的是，每座山都会给出相同的组合阴影：晶体B（Infty）和Mirkovic-Vilonen多面体。为了区分这三个基础，我们引入了这些多面体支持的措施。我们还报告了这些碱基与最大单位亚组坐标环上的簇结构的相互作用。
In order to give a combinatorial descriptions of tensor product multiplicites for semisimple groups, it is useful to find bases for representations which are compatible with the actions of Chevalley generators of the Lie algebra. There are three known examples of such bases, each of which flows from geometric or algebraic mountain. Remarkably, each mountain gives the same combinatorial shadow: the crystal B(infty) and the Mirkovic-Vilonen polytopes. In order to distinguish between the three bases, we introduce measures supported on these polytopes. We also report on the interaction of these bases with the cluster structure on the coordinate ring of the maximal unipotent subgroup.
