Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry

A. Hutsalyuk; A. Liashyk; E. Ragoucy; N. A. Slavnov; S. Z. Pakuliak

Scalar products of Bethe vectors in the models with mathfrak{gl}(m|n) symmetry

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arxiv 1704.08173 v3 pith:LJIBD3CZ submitted 2017-04-26 math-ph math.MP

Scalar products of Bethe vectors in the models with mathfrak{gl}(m|n) symmetry

A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov This is my paper

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We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by $\mathfrak{gl}(m|n)$ superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of Bethe parameters. We also obtain recursions for the Bethe vectors. This allows us to find recursions for the highest coefficient of the scalar product.

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Yangian Doubles and off-Shell Bethe Vectors
nlin.SI 2026-07 unverdicted novelty 6.0

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.