Accessibility of Nilpotent Orbits in Classical Algebras

Abstract

Let $G$ be a classical linear algebraic group over an algebraically closed field, and let $\mathfrak{n}$ denote the subset of nilpotent elements in its Lie algebra. In this paper we study a partial order on the $G$-orbits in $\mathfrak{n}$ given by taking limits along cocharacters of $G$. This gives rise to the so-called accessibility order on the nilpotent orbits. Our main results show that for general and special linear algebras, this new order coincides with the usual dominance order on nilpotent orbits, but for symplectic and orthogonal algebras this is not the case.