A combinatorial characterization of the annihilator varieties of highest weight modules for classical Lie algebras

Abstract

Let $\mathfrak{g}$ be a classical Lie algebra. Let $L(\lambda)$ be a highest weight module of $\mathfrak{g}$ with highest weight $\lambda-\rho$, where $\rho$ is half the sum of positive roots. In 1985, Joseph proved that the associated variety of a primitive ideal is the Zariski closure of a nilpotent orbit in $\mathfrak{g}^*$. In this paper, we will give some combinatorial characterizations of the annihilator varieties of highest weight modules for classical Lie algebras. In fact, we will give two algorithms, i.e., bipartition algorithm and partition algorithm.Comment: 40page