An−1(1) reflection K-matrices Original Research Article

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the An−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 K-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.