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

TL;DR

The paper introduces an algorithm based on an infinite Robinson-Schensted algorithm to compute primitive ideals of the universal enveloping algebra of the infinite-dimensional Lie algebra sl(∞), advancing understanding of its representation theory.

Contribution

It develops a novel infinite Robinson-Schensted algorithm to determine annihilators of simple highest weight modules in U(sl(∞)), providing new computational tools.

Findings

Algorithm successfully computes annihilators for simple modules.

Connects combinatorial algorithms with infinite-dimensional Lie algebra representations.

Enhances understanding of primitive ideals in U(sl(∞)).

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.