  Linear differential algebraic groups (LDAGs) measure differential algebraic
dependencies among solutions of linear differential and difference equations
with parameters, for which LDAGs are Galois groups. The differential
representation theory is a key to developing algorithms computing these groups.
In the rational representation theory of algebraic groups, one starts with
SL(2) and tori to develop the rest of the theory. In this paper, we give an
explicit description of differential representations of tori and differential
extensions of irreducible representation of SL(2). In these extensions, the two
irreducible representations can be non-isomorphic. This is in contrast to
differential representations of tori, which turn out to be direct sums of
isotypic representations.
