Representations of Super W(2,2) algebra mathfrak{L}

In paper, we study the representation theory of super $W(2,2)$ algebra ${\mathfrak{L}}$. We prove that ${\mathfrak{L}}$ has no mixed irreducible modules and give the classification of irreducible modules of intermediate series. We determinate the conjugate-linear anti-involution of ${\mathfrak{L}}$ and give the unitary modules of intermediate series.