Let $V_k(\mathbb{R}^n)$ be the Stiefel manifold of $k$-frames in $\mathbb{R}^n$. The symmetric group of $k$ letters $\Sigma_k$ acts freely by permuting vectors in $k$-frames.
Does the quotient $V_k(\mathbb{R}^n)/\Sigma_k$ have a name?
This space seems to play an important role in the problem of $k$-regular embeddings. For example, seethis paper. But I've never heard of its name.
