5 problems

Let $L$ and $\hat{L}$ be the two lattices in the prehomogeneous vector space whose zeta functions are $\xi_i(L,s)$ and $\xi_i(\hat{L},s)$ for $i=1,2,3$, as defined in the paper. Oh…

Let $(\mathrm{G},V)$ be a strongly prehomogeneous vector space, meaning an algebraic group $\mathrm{G}$ acts linearly on a finite-dimensional vector space $V$ with finitely many or…

Let $(\mathrm{G},V)$ be a prehomogeneous vector space, let $Z\subset V$ be the closure of an orbit of $\mathrm{G}$, and write $Z_{\mathrm{sing}}$ for its singular locus. For an int…

Let $(\mathrm{G},V)$ be a prehomogeneous vector space, meaning that a reductive linear group $\mathrm{G}$ acts on the finite-dimensional vector space $V$ with a dense orbit. Let…

Let $G$ be an algebraic group, let $P$ be a parabolic subgroup with unipotent radical $N$, and let $C$ be a conjugacy class in $P/N$. Let $D$ be the inflation of $C$ to $P$, and le…