Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type

Details Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type

2008-10-12

arxiv.org/abs/0810.2068v2

SIGMA 5 (2009), 012, 27 pages

Mathematics

Representation Theory

Scientific paper

10.3842/SIGMA.2009.012

We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is yet a third algebra containing a spin Weyl group algebra which is Morita (super)equivalent to the above two algebras. We establish the PBW properties and construct Verma-type representations via Dunkl operators for these algebras.

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