This is a follow-up of this previous question below:
Intersections of $B$ and $B^-$ orbits in the flag variety $G/B$
Let $G = SL_n(\mathbb{C})$, $B$ be the standard Borel subgroup, and consider some other Borel subgroups $wBw^{-1}$, for some $w$ in the Weyl group $W$. When $w$ is the longest element $w_0$, we have $wBw^{-1}$ is just the opposite Borel $B^-$.
How much is known about the geometry of the intersections of the $B$ and $wBw^{-1}$ orbits? I know that the intersection will not be transverse except when $w = w_0$. Are these intersections affine? Are they equi-dimensional? What are their dimensions? Any references?
