Finite growth representations of infinite Lie conformal algebras

We classify all finite growth representations of all infinite rank subalgebras of the Lie conformal algebra gc_1 that contain a Virasoro subalgebra.Comment: 22 page

Integrable highest weight modules over affine superalgebras and Appell's function

We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level~1 case. The analysis of this construction shows, in particular, that in the simplest case of the $s\ell (2|1)$ level~1 affine superalgebra the characters are expressed in terms of the Appell elliptic function. Our results demonstrate that the representation theory of affine Lie superalgebras is quite different from that of affine Lie algebras.Comment: 54 page