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Hecke–Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: spin Hecke algebras; Hecke–Clifford algebras; Dunkl operators. 
@article{SIGMA_2009_5_a11,
     author = {Ta Khongsap and Weiqiang Wang},
     title = {Hecke{\textendash}Clifford {Algebras} and {Spin} {Hecke} {Algebras~IV:} {Odd} {Double} {Affine} {Type}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2009},
     volume = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a11/}
}
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Ta Khongsap; Weiqiang Wang. Hecke–Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a11/

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