$\mathbb{P}{\mathfrak{gl}}_2$ is Multiplicity-Free as a $PG{L}_2\times PG{L}_2$-Variety

Dmitry Gourevitch, Shai Keidar

Let $F$ be a non-Archimedean local field. Let $G$ be an algebraic group over $F$. A $G$-variety $X$ defined over $F$ is said to be multiplicity-free if for any admissible irreducib…