# Conjugacy classes with elliptic limit points

Let $G$ be a reductive algebraic group over $\mathbb R$ and $K$ a maximal compact subgroup. Then we refer to the conjugacy class in $G$ of some $k \in K$ as an elliptic conjugacy class.

Question: Can one characterizes those conjugacy classes in $G$ which contain an elliptic conjugacy class in their closure?

(For $G = GL_n(\mathbb R)$ they are characterized by the fact that all eigenvalues are of modulus one, if I a not mistaken.)

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