The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold. There is a conjecture for how to calculate the index. In this paper we give an affirmative answer to this conjecture for the exceptional Riemannian symmetric spaces and for the classical symmetric spaces Sp$_r(\mathbb R)/U_r$. Our methodology is new and based on the idea of using slice representations for studying totally geodesic submanifolds.

中文翻译：

---

异常对称空间的索引

黎曼对称空间的指数是适当的全测地子流形的最小余维。关于如何计算指数有一个猜想。在本文中，我们对异常黎曼对称空间和经典对称空间 Sp$_r(\mathbb R)/U_r$ 的这个猜想给出了肯定的答案。我们的方法是新的，基于使用切片表示来研究完全测地线子流形的想法。