Simple weight modules for Yangian Y(2).

Let be a finite-dimensional simple Lie algebra over ℂ. A Y () -module is said to be weight if it is a weight -module. We give a complete classification of simple weight modules for Y ( 2) which admits a one-dimensional weight space. We prove that there are four classes of such modules: finite, highest weight, lowest weight and dense modules. Different from the classical 2 -representation theory, we show that there exists a class of Y ( 2) irreducible modules which have uniformly two-dimensional weight spaces. [ABSTRACT FROM AUTHOR]