Primitive ideals of $\mathrm{U}(\mathfrak{sl}(\infty ))$ and the Robinson-Schensted algorithm at infinity

Abstract

We present an algorithm which computes the annihilator in $\mathrm{U}(\mathfrak{sl}(\infty ))$ of any simple highest weight $\mathfrak{sl}(\infty )$-module $L_{\mathfrak{b}}(\lambda )$. This algorithm is based on an infinite version of the Robinson-Schensted algorithm.