Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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