  Series of finite dimensional representations of the superalgebras spl(p,q)
can be formulated in terms of linear differential operators acting on a
suitable space of polynomials. We sketch the general ingredients necessary to
construct these representations and present examples related to spl(2,1) and
spl(2,2). By revisiting the products of projectivised representations of sl(2),
we are able to construct new sets of differential operators preserving some
space of polynomials in two or more variables. In particular, this allows to
express the representation of spl(2,1) in terms of matrix differential
operators in two variables. The corresponding operators provide the building
blocks for the construction of quasi exactly solvable systems of two and four
equations in two variables. We also present a quommutator deformation of
spl(2,1) which, by construction, provides an appropriate basis for analyzing
the quasi exactly solvable systems of finite difference equations.
