  We discuss irreducible highest weight representations of the sl(2) loop
algebra and reducible indecomposable ones in association with the sl(2) loop
algebra symmetry of the six-vertex model at roots of unity. We formulate an
elementary proof that every highest weight representation with distinct
evaluation parameters is irreducible. We present a general criteria for a
highest weight representation to be irreducble. We also give an example of a
reducible indecomposable highest weight representation and discuss its
dimensionality.
