3 problems

Let $K$ act on the ambient flag variety, let $Y_{\gamma}$ be the closure of the orbit indexed by $\gamma$, and let $\mathcal{O}_{\alpha}$ be the orbit indexed by $\alpha$ with…

Pattern-avoidance equivalence conjecture. In types $AI$ and $AII$, an involution $\pi$ avoids all bad patterns in the sense of this section if and only if it avoids all bad pattern…

Let $G=GL(m,\mathbb C)$, let $G/B$ be its flag variety, and let $\mathcal O_\pi$ be a $K$-orbit with closure $\overline{\mathcal O}_\pi$. Let $w_0$ denote the longest element, and…