Current presentation for the super-Yangian double $DY\left(gl\right(m|n\left)\right)$ and Bethe vectors

Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians $Y\left(gl\right(m|n)$ in terms of the current generators of the Yangian double $DY\left(gl\right(m|n\left)\right)$. The method of projections onto intersections of different types of Borel subalgebras of this infinite-dimensional algebra is used to construct the Bethe vectors. Calculation of these projections makes it possible to express the supersymmetric Bethe vectors in terms of the matrix elements of the universal monodromy matrix. Two different presentations for the Bethe vectors are obtained by using two different but isomorphic current realizations of the Yangian double $DY\left(gl\right(m|n\left)\right)$. These Bethe vectors are also shown to obey certain recursion relations which prove their equivalence.

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