Universally defined representations of Lie conformal superalgebras

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined representation of a conformal Lie (super)algebra L is completely determined by commutation relations of L and by the requirement of associative locality of generators. We describe such representations for conformal superalgebras Wn, n ≥ 0, with respect to a natural set of generators. We also consider the problem for superalgebras Kn. In particular, we find a universally defined representation for the Neveu–Schwartz conformal superalgebra K1 and show that the analogues of this representation for n ≥ 2 are not universally defined.