Non-weight Modules and Harish-Chandra Modules for a Subalgebra of N = 2 Superconformal Algebra

Abstract

The algebra $\frak{q}_{\varepsilon}$ is a subalgebra of both the Ramond and Neveu-Schwarz sectors of the N = 2 superconformal algebra, with its even part being the Heisenberg-Virasoro algebra. Based on their previous work on simple Whittaker modules over the algebra $\frak{q}_{\varepsilon}$, the authors construct and analyze two categories of non-weight modules for the algebra $\frak{q}_{\varepsilon}$. The first category consists of modules whose restriction to the universal enveloping algebra of the Cartan subalgebra (modulo the center) is free of rank 1. The second category involves modules whose restriction to the universal enveloping algebra of a subalgebra larger than Cartan subalgebra is free of rank 1. In particular, the authors determine the isomorphism classes and irreducibility of these modules and classify all simple cuspidal modules and then classify all simple Harish-Chandra modules for the algebra $\frak{q}_{\varepsilon}$.

Keywords

Non-weight module / Harish-Chandra module / Simple module / N = 2 superconformal algebra / 17B10

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