Bethe vectors in integrable models based on the super-Yangian Y(gl(m|n)) Y(gl(m|n))

Lyashik Andrey, Arthur Hutsalyuk, Stanislav Zdislavovich Pakuliak, E. Ragoucy, N. A. Slavnov

Published Jan 1, 2016• 0 citations

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Bethe vectors for models based on the super-Yangian Y(gl(m|n))

Pakuliak, S. Z., E. Ragoucy, N. A. Slavnov

We study Bethe vectors of integrable models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$ . Starting from the super-trace formula, we exhibitrecursion 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 explicitexpressions 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 Bethevectors, and, for $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$ super-Yangians, show recursion relations for them. Again, the latter allow usto get explicit expressions for dual Bethe vectors.We study Bethe vectors of integrable models based on the super-Yangian$Y(\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibitrecursion 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 explicitexpressions 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 Bethevectors, and, for $Y(\mathfrak{gl}(2|1))$ and $Y(\mathfrak{gl}(1|2))$super-Yangians, show recursion relations for them. Again, the latter allow usto get explicit expressions for dual Bethe vectors.

Jan 1, 20171 citation

We study Bethe vectors of integrable models based on the super-Yangian

Y(\mathfrak{gl}(m|n))

. Starting from the super-trace formula, we exhibitrecursion 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 explicitexpressions 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 Bethevectors, and, for

Y(\mathfrak{gl}(2|1))

and

Y(\mathfrak{gl}(1|2))

super-Yangians, show recursion relations for them. Again, the latter allow usto get explicit expressions for dual Bethe vectors.