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arXiv · 1604.02311

Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$

S. Z. Pakuliak·E. Ragoucy·N. A. Slavnov
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Abstract

We study Bethe vectors of integrable models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$. These recursion relations allow to get explicit expressions for the Bethe vectors. Using an antimorphism of the super-Yangian $Y(\mathfrak{gl}(m|n))$, we also construct a super-trace formula for dual Bethe vectors, and, for $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$ super-Yangians, show recursion relations for them. Again, the latter allow us to get explicit expressions for dual Bethe vectors.

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S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov. 2016-05-27. Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$. https://doi.org/10.1093/integr%2Fxyx001

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