Harish-Chandra Modules of the Intermediate Series over the Topological N = 2 Superconformal Algebra

Abstract

The topological N = 2 superconformal algebra was introduced by Dijkgraaf, Verlinde and Verlinde as the symmetry algebra of topological strings at d < 1. We give a classification of irreducible 𝕫 × 𝕫-graded modules of the intermediate series over this infinite-dimensional Lie superalgebra.

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

“…It is known that representations of the superconformal algebras get more and more complicated with increasing the number of fermionic currents N. The classification of all simple Harish-Chandra modules over the N = 1 and untwisted N = 2 superconformal algebras was achieved respectively in [21,16]. Moreover, some special weight modules over the N = 2 superconformal algebras were studied (see [8,11,14,19,25]).…”