Abstract: One kind of representation of a spin group is obtained by restricting either a complex or real representation of the Clifford algebra to its spin group. It plays an important role in constructing generalized Dirac operators. In this talk, we will construct regular and spin representations of complex Clifford algebras. The former is a reducible representation given by Clifford multiplication on the exterior algebra and the latter is an irreducible representation on the exterior algebra of a complex polarization, also known as the polarized Fock space.