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SIGMA 5 (2009), 012, 27 pages arXiv:0810.2068
https://doi.org/10.3842/SIGMA.2009.012
Contribution to the Special Issue on Dunkl Operators and Related Topics
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
Ta Khongsap and Weiqiang Wang
Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA
Received October 15, 2008, in final form January 22, 2009; Published online January 28, 2009
Abstract
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.
Key words:
spin Hecke algebras; Hecke-Clifford algebras; Dunkl operators.
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