3 problems

Let $K\subset G$ be the symmetric subgroup of a real form $G_{\mathbb R}\subset G$. Write $X({\mathcal K})$ for the corresponding symmetric variety, $G({\mathcal O})$ for the posit…

Let $(\operatorname{G},\mathrm{H})$ be a symmetric pair over $k$ such that $\operatorname{G}$ is quasi-split over $k$ and $\operatorname{G}_{\mathrm{der}}$ is simply connected. Set…

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…