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

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

2011-12-05

arxiv.org/abs/1112.0839v1

Physics

Mathematical Physics

30 pages

Scientific paper

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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