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

Abstract

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