Asymptotic representations and Drinfeld rational fractions

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 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.