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arXiv · 0810.2068

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

Ta Khongsap·Weiqiang Wang
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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.

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BibTeXRIS

Ta Khongsap, Weiqiang Wang. 2009-01-28. Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type. https://doi.org/10.3842/sigma.2009.012

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