3 problems

Let $G$ be a connected semisimple group, let $P$ be a parabolic subgroup of $G$, and let $U_P$ be its unipotent radical. Let $B$ be a Borel subgroup and set … as a homogeneous vect…

The orbit classification conjecture. Two $G$-orbits $\mathcal{O}$ and $\mathcal{O}'$ lie in the same $\mathrm{Aut}(X)^0$-orbit if and only if

Let $X$ be a horospherical complexity-zero variety, let $\tau$ be a face of its cone $\sigma^\vee$, and let $O_\tau$ be the corresponding $G$-orbit. Let $p_1,\ldots,p_k$ be the pri…