On representations of the affine superalgebra $\mathbb q(n)^{(2)}$

In this paper we study highest weight representations of the affine Lie superalgebra $\mathbb q(n)^{(2)}$. We prove that any Verma module over this algebra is reducible and calculate the character of an irreducible $\mathbb q(n)^{(2)}$-module with a generic highest weight. This formula is analogous to the Kac–Kazhdan formula for generic irreducible modules over affine Lie algebras at the critical level.