Simple Harish-Chandra modules over the super affine-Virasoro algebras

Abstract

In this paper, we classify all simple Harish-Chandra modules over the super affine-Virasoro algebra $\hat{\mathcal{L}}=\mathcal{W}⋉(\mathfrak{g}\otimes \mathcal{A})\oplus \mathbb{C}C$, where $\mathcal{A}=\mathbb{C}[t^{\pm 1}]\otimes \hat{I}›(1)$ is the tensor superalgebra of the Laurent polynomial algebra in even variable $t$ and the Grassmann algebra in odd variable $\hat{I}¾$, $\mathcal{W}$ is the Lie superalgebra of superderivations of $\mathcal{A}$, and $\mathfrak{g}$ is a finite-dimensional perfect Lie superalgebra.