Representations of untwisted loop N = 2 superconformal algebras

In this paper, we construct a class of non-weight modules of untwisted loop N = 2 superconformal algebras R , which are the loop version of the modules defined in [30] and [4] . Denote h ± = C L 0 , 0 ⊕ C G 0 , 0 ± . We give a classification of R -modules such that when considered as modules of U ( h ± ) they are free of rank 1. A sufficient and necessary condition for such modules to be simple is provided. Moreover, we determine the isomorphism classes of these modules. At last, by using the weighting functor, we derive the intermediate series modules from these non-weight R -modules.