Classification of Harish-Chandra modules over the $W$-algebra W(2,2)

Abstract

In this paper, we classify all irreducible weight modules with finite dimensional weight spaces over the $W$-algebra $W(2, 2)$. Meanwhile, all indecomposable modules with one dimensional weight spaces over the $W$-algebra $W(2, 2)$ are also determined.

Latex, 20 pages