Mathematical Research Letters

Volume 16 (2009)

Number 6

Double affine Hecke algebras for the spin symmetric group

Pages: 1071 – 1085

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n6.a14

Author

Weiqiang Wang (University of Virginia)

Abstract

We introduce a new class (in two versions, $\An$ and $\Bn$) 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.

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