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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
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
Citation:
Ta Khongsap, Weiqiang Wang, “Hecke–Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type”, SIGMA, 5 (2009), 012, 27 pp.
Linking options:
https://www.mathnet.ru/eng/sigma358 https://www.mathnet.ru/eng/sigma/v5/p12
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