  We introduce a new class (in two versions) of rational double affine Hecke
algebras (DaHa) associated to the spin symmetric group. We establish the basic
properties of the algebras, such as PBW and Dunkl representation, and
connections to Nazarov's degenerate affine Hecke-Clifford algebra and to a new
degenerate affine Hecke algebra introduced here. We formulate a Morita
equivalence between the two versions of rational DaHa's. The trigonometric
generalization of the above constructions is also formulated and its relation
to the rational counterpart is established.

Representation Theory;Quantum Algebra