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?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.