  We develop and collect techniques for determining Hochschild cohomology of
skew group algebras S(V)#G and apply our results to graded Hecke algebras. We
discuss the explicit computation of certain types of invariants under
centralizer subgroups, focusing on the infinite family of complex reflection
groups G(r,p,n) to illustrate our ideas. Resulting formulas for Hochschild
two-cocycles give information about deformations of S(V)#G and, in particular,
about graded Hecke algebras. We expand the definition of a graded Hecke algebra
to allow a nonfaithful action of G on V, and we show that there exist
nontrivial graded Hecke algebras for G(r,1,n), in constrast to the case of the
natural reflection representation. We prove that one of these graded Hecke
algebras is equivalent to an algebra that has appeared before in a different
form.
