Abstract
The Yangian Y(gln+1) for the general linear Lie algebra gln+1 contains U(gln+1) as a subalgebra. Let h denote the Lie subalgebra of gln+1 generated by trace-zero matrices. We study the category M(Y(gln+1),U(h)) consisting of Y(gln+1)-modules whose restriction to U(h) is free of rank 1. We classify the isomorphism classes of objects in this category and determine the simplicity of these modules. Additionally, we demonstrate that these modules have central characters.
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