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

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