The pair $(x,y)$ is a parameter for a representation of $G$…
The pair $(x,y)$ is a parameter for a representation of $G$ (so the negative transpose of the involution of $H$ associated to $x$ is the one of $H^\vee$ associated to $y$.)
The pair $(x,y)$ is a parameter for a representation of $G$ (so the negative transpose of the involution of $H$ associated to $x$ is the one of $H^\vee$ associated to $y$.)