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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 012, 27 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.012 (Mi sigma358) 		 
This article is cited in 10 scientific papers (total in 10 papers)

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

Ta Khongsap, Weiqiang Wang

Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA
Full-text PDF (398 kB) Citations (10)
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DOI: https://doi.org/10.3842/SIGMA.2009.012
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.
Keywords: spin Hecke algebras; Hecke–Clifford algebras; Dunkl operators.
Received: October 15, 2008; in final form January 22, 2009; Published online January 28, 2009
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Document Type: Article
MSC: 20C08
Language: English
Citation: Ta Khongsap, Weiqiang Wang, “Hecke–Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type”, SIGMA, 5 (2009), 012, 27 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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