Monomial bases for quantum affine sln

We use the idea of generic extensions to investigate the correspondence between the isomorphism classes of nilpotent representations of a cyclic quiver and the orbits in the corresponding representation varieties. We endow the set M of such isoclasses with a monoid structure and identify the submonoid Mc generated by simple modules. On the other hand, we use the partial ordering on the orbits (i.e., the Bruhat-Chevalley type ordering) to induce a poset structure on M and describe the poset ideals generated by an element of the submonoid Mc in terms of the existence of a certain composition series of the corresponding module. As applications of these results, we generalize some results of Ringel involving special words to results with no restriction on words and obtain a systematic description of many monomial bases for any given quantum affine sln.