Simple Harish-Chandra modules over the superconformal current algebra.

In this paper, we classify the simple Harish-Chandra modules over the superconformal current algebra g ˆ , which is the semi-direct sum of the N = 1 superconformal algebra with the affine Lie superalgebra g ˙ ⊗ A ⊕ C C 1 , where g ˙ is a finite-dimensional simple Lie algebra, and A is the tensor product of the Laurent polynomial algebra and the Grassmann algebra. As an application, we can directly get the classification of the simple Harish-Chandra modules over the N = 1 Heisenberg-Virasoro algebra. [ABSTRACT FROM AUTHOR]