$\newcommand{\R}{\mathbb{R}}$
$\newcommand{\C}{\mathbb{C}}$
$\newcommand{\rank}{\operatorname{rank}}$
$\newcommand{\N}{\mathbb{N}}$
$\newcommand{\Z}{\mathbb{Z}}$
$\newcommand{\K}{\mathbb{K}}$
$\newcommand{\Ha}{\mathbb{H}}$
$\newcommand{\act}{\curvearrowright}$
$\newcommand{\mfp}{\frak{p}}$
$\newcommand{\Herm}{\operatorname{Herm}}$
$\newcommand{\Alt}{\operatorname{Alt}}$
$\newcommand{\Sym}{\operatorname{Sym}}$
$\newcommand{\trace}{\operatorname{trace}}$
$\newcommand{\Ad}{\operatorname{Ad}}$
$\newcommand{\ad}{\operatorname{ad}}$
$\newcommand{\diag}{\operatorname{diag}}$
$\newcommand{\Pf}{\operatorname{Pf}}$
$\newcommand{\Lie}{\operatorname{Lie}}$
$\renewcommand{\labelenumi}{(\roman{enumi})}$
