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We present the classification of the most general regular solutions to theboundary Yang-Baxter equations for vertex models associated withnon-exceptional affine Lie algebras. Reduced solutions found by applying alimit procedure to the general solutions are discussed. We also present thelist of diagonal $K$-matrices. Special cases are considered separately.Comment: 58 pages, revised version, references added, LaTe

On , , , , , , and reflectionK-matrices