  We give a fully explicit description of Lie algebra derivatives (generalizing
raising and lowering operators) for representations of SL(3,R) in terms of a
basis of Wigner functions. This basis is natural from the point of view of
principal series representations, as well as computations in the analytic
theory of automorphic forms (e.g., with Whittaker functions). The method is
based on the Clebsch-Gordan multiplication rule for Wigner functions, and
applies to other Lie groups whose maximal compact subgroup is isogenous to a
product of SU(2) and U(1) factors. As an application, we give a complete and
explicit description of the K-type structure of certain cohomological
representations.
