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

Quantum Reduction and Representation Theory of Superconformal Algebras

We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all superconformal algebras.Comment: 48 page

Infinite dimensional primitive linearly compact Lie superalgebras

We classify open maximal subalgebras of all infinite-dimensional linearly compact simple Lie superalgebras. This is applied to the classification of infinite-dimensional Lie superalgebras of vector fields, acting transitively and primitively in a formal neighborhood of a point of a finite-dimensional supermanifold.Comment: 99 page