Irreducible twisted Yangian module structures on a commutative subalgebra

The twisted Yangian [Formula: see text] associated with [Formula: see text] contains [Formula: see text] as a subalgebra. Let [Formula: see text] denote the Cartan subalgebra of [Formula: see text] We study the category [Formula: see text] consisting of [Formula: see text]-modules whose restriction to [Formula: see text] is free of rank 1. We classify the isomorphism classes of objects within this category and demonstrate that these objects have central characters.