Loop groups and the path model (B04)

该项目旨在对表示论中的组合路径模型进行几何重新解释。其目的是融合关于半单李代数及其组合模型表示基的几何和拓扑构造的不同观点。这些观点之一是辛；它是基于对Mirković-Vilonen多面体的研究，它表征了这样的基，并产生了像下动量图的相关基。变分方法是通过关于环群的Morse理论进入的。

The project intends to give a geometric reinterpretation of the combinatorial path model in representation theory. The aim is to merge various points of view on the geometric and topological construction of bases of representations of semisimple Lie algebras and their associated combinatorial models. One of these points of view is symplectic; it is based on the study of Mirković-Vilonen polytopes, which characterize one such basis and arise as the image under the momentum map of the relevant basis. Variational methods enter via Morse theory on loop groups.