$A_{n-1}^{(1)}$ Reflection K-Matrices

Abstract

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $A_{n-1}^{(1)}$ affine Lie algebra. We have classified them in two classes of solutions. The first class consists of $n(n-1)/2$ K-matrix solutions with three free parameters. The second class are solutions that depend on the parity of $n$. For $n$ odd there exist $n$ reflection matrices with $2+[n/2]$ free parameters. It turns out that for $n$ even there exist $n/2$ K-matrices with $2+n/2$ free parameters and $n/2$ K-matrices with $1+n/2$ free parameters.

19 pages, LaTex

References in corpus (3)

• Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line
• Boundary quantum group generators of type A
• D_{n+1}^(2) Reflection K-matrices

Cited by in corpus (15)

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• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
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• $C_n^{(1)}$, $D_n^{(1)}$ and $A_{2n-1}^{(2)}$ reflection K-matrices
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• Gauge Theory and Boundary Integrability II: Elliptic and Trigonometric Case
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• Spectral equivalences and symmetry breaking in integrable SU_q(N) spin chains with boundaries
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