关于有理K-矩阵的分类
On the classification of rational K-matrices
摘要：
本文给出了有理K-矩阵在“经典极限”（谱参数趋于无穷大）可逆的可能剩余对称性的一个推导。该推导仅使用边界Yang-Baxter方程和R-矩阵的渐近展开式。证明了文献中的假设：如果原对称代数和剩余对称代数分别为$\mathfrak{g}$和$\mathfrak{h}$，则存在$\mathfrak{g}$的李代数对合，其不变子代数为$\mathfrak{h}$ .此外，我们还研究了在“经典极限”下不可逆的K-矩阵。证明了它们的对称代数不是约化的，而是约化的可解李代数的半直和。
英文摘要：
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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