On non-weight representations of the $N=2$ superconformal algebras

Abstract

In this paper, we construct a family of non-weight modules over the untwisted N = 2 superconformal algebras. Those modules when regarded as modules over the Cartan subalgebra are free of rank 2. We give a classification of isomorphism classes of such modules. Moreover, all submodules of such modules are precisely determined. In particular, those modules we construct are not simple.

Non-weight modules over the super-BMS$_3$ algebra

“…In [16], the free U(h)-modules of rank 1 over the Ramond N = 1 algebra and free U(h)-modules of rank 2 over the Neveu-Schwarz N = 1 algebra were respectively classified. Recently, a family of non-weight modules over the untwisted N = 2 superconformal algebras were constructed in [17], which regarded as modules over the Cartan subalgebra are free of rank 2. In this paper, we aim to study free U(h)-modules and U(H)-modules respectively over the Ramond type and Neveu-Schwarz type of super-BMS 3 algebras.…”