  We introduce and study a category of representations of the Borel algebra,
associated with a quantum loop algebra of non-twisted type. We construct
fundamental representations for this category as a limit of the
Kirillov-Reshetikhin modules over the quantum loop algebra and we establish
explicit formulas for their characters. We prove that general simple modules in
this category are classified by n-tuples of rational functions in one variable,
which are regular and non-zero at the origin but may have a zero or a pole at
infinity.
