  In this paper, we define two generalisations of Dirac operators for
Drinfeld's Hecke algebra. One generalisation, Parthasarathy operators inherit
the notion of the Dirac inequality. The second generalisation, warped Dirac
operators are such that every unitary module must have a non-zero warped Dirac
cohomology. An open question is whether non-zero warped Dirac cohomology can
determine the infinitesimal character akin to the fact that non-zero Dirac
cohomology does. For a type $A$ Hecke algebra we give a family of operators in
each class.
