Boundary K-matrices for the six vertex and the n(2n-1)An-1 vertex models

Boundary conditions compatible with integrability are obtained for two-dimensional models by solving the factorizability equations for the reflection matrices K+or-( theta ). For the six vertex model the general solution depending on four arbitrary parameters is found. For the An-1 models all diagonal solutions are found. The associated integrable magnetic Hamiltonians are explicitly derived.