Let $G = SL_n(\mathbb{C})$, $B$ be a Borel subgroup, and $B^-$ be the opposite Borel.

Both the $B$ and $B^-$ orbits on the flag variety $G/B$ are indexed by the Weyl group $W$. Let $S_{w_1}$ and $S^-_{w_2}$ denote the $B$ and $B^-$ orbit corresponding to $w_1, w_2 \in W$ respectively.

So how much is known about the intersections of $B$ and $B^-$ orbits $S_{w_1} \cap S^-_{w_2}$ in the flag variety $G/B$? Are these intersections affine? Are they equi-dimensional? What are their dimensions?