Geometry of spinors in 14 dimensions

14维的自旋是例外的，因为它们与八元数密切相关。当这个维上存在Majorana-Weyl旋量时，有两个特征，即(7，7)和(11，3)。前一种情况的研究动机来自广义几何，在一定程度上理解了Majorana-Weyl自旋空间中的自旋(7，7)轨道。后一种情况在很大程度上是一个悬而未决的问题。本项目将致力于完成(7，7)案例中未回答的问题，并提供(11，3)案例中的轨道分类。这个项目的动机是，在这两种情况下，一代SM费米子的全部内容都可以由这样的Majorana-Weyl旋量编码。人们感兴趣的主要问题是，这些自旋定义的丰富几何结构是否与人们在粒子物理学的SM中找到的结构有关。

Spinors in 14 dimensions are exceptional because they are intimately linked to the octonions. There are two signatures when Majorana-Weyl spinors in this dimension exist, namely (7,7) and (11,3). The former case has been studied with motivations coming from generalised geometry, and Spin(7,7) orbits in the space of Majorana-Weyl spinors to an extent understood. The latter case is to a very large degree an open question. This project will aim to complete the questions left unanswered in the (7,7) case and provide a classification of the orbits in the (11,3) case. The motivations for this project are in the fact that in both cases the full content of one generation of the SM fermions can be encoded by such a Majorana-Weyl spinor. The main question of interest is whether the rich geometric structures that such spinors define has anything to do with the structures one finds in the SM of particle physics.