Off-shell Bethe vectors are constructed via Yangian double currents and verified to satisfy defining properties previously used for on-shell vectors in ggo-invariant models.
Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
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abstract
We find Bethe vectors for quantum integrable models associated with the supersymmetric Yangians $Y(\mathfrak{gl}(m|n)$ in terms of the current generators of the Yangian double $DY(\mathfrak{gl}(m|n))$. More specifically, we use the method of projections onto intersections of different type Borel subalgebras in this infinite dimensional algebra to construct the Bethe vectors. Calculating these projection the supersymmetric Bethe vectors can be expressed through matrix elements of the universal monodromy matrix elements. Using two different but isomorphic current realizations of the Yangian double $DY(\mathfrak{gl}(m|n))$ we obtain two different presentations for the Bethe vectors. These Bethe vectors are also shown to obey some recursion relations which prove their equivalence.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Serre relations in Yangian doubles are reformulated as quadratic commutation relations between composed currents for classical Lie algebras.
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Yangian Doubles and off-Shell Bethe Vectors
Off-shell Bethe vectors are constructed via Yangian double currents and verified to satisfy defining properties previously used for on-shell vectors in ggo-invariant models.
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Serre Relations in Yangian Doubles
Serre relations in Yangian doubles are reformulated as quadratic commutation relations between composed currents for classical Lie algebras.