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arXiv · 1112.0839

On factorizing $F$-matrices in $Y(sl_n)$ and $U_q(\hat{sl_n})$ spin chains

S. G. Mc Ateer·M. Wheeler
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Abstract

We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de Santos, we derive a completely factorized expression for the $F$-matrix of such models and prove its equivalence to the expression obtained by Albert, Boos, Flume and Ruhlig. A new relation between the $F$-matrices and the Bethe eigenvectors of these spin chains is given.

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S. G. Mc Ateer, M. Wheeler. 2011-12-05. On factorizing $F$-matrices in $Y(sl_n)$ and $U_q(\hat{sl_n})$ spin chains. https://doi.org/10.1088/1742-5468%2F2012%2F04%2Fp04016

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