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arXiv · 1904.03044

On the classification of rational K-matrices

Tamas Gombor
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Abstract

This paper presents a derivation of the possible residual symmetries of rational K-matrices which are invertible in the ''classical limit'' (the spectral parameter goes to infinity). This derivation uses only the boundary Yang-Baxter equation and the asymptotic expansions of the R-matrices. The result proves the previous assumption of the literature: if the original and the residual symmetry algebras are $\mathfrak{g}$ and $\mathfrak{h}$ then there exists a Lie-algebra involution of $\mathfrak{g}$ for which the invariant sub-algebra is $\mathfrak{h}$. In addition, we study some K-matrices which are not invertible in the ''classical limit''. It is shown that their symmetry algebra is not reductive but a semi-direct sum of reductive and solvable Lie-algebras.

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Tamas Gombor. 2019-04-05. On the classification of rational K-matrices. https://doi.org/10.1088/1751-8121%2Fab7602

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