Double Affine Hecke Algebras for the Spin Symmetric Group
نویسنده
چکیده
We introduce a new class (in two versions, Au and Bu) 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 algebra and to a new degenerate affine Hecke algebra introduced here. We formulate a precise connection between the two versions of rational DaHa’s. The trigonometric generalization of the above and its relations to the rational counterpart are also established.
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