Khongsap, Ta; Wang, Weiqiang Hecke-Clifford algebras and spin Hecke algebras. IV: Odd double affine type. (English) Zbl 1187.20002 SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 012, 27 p. (2009). Summary: 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 is 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. For part III cf. the first author, J. Algebra 322, No. 8, 2731-2750 (2009; Zbl 1182.20006). Cited in 6 Documents MSC: 20C08 Hecke algebras and their representations 20F55 Reflection and Coxeter groups (group-theoretic aspects) Keywords:spin Hecke algebras; Hecke-Clifford algebras; Dunkl operators; Weyl groups; double affine Hecke algebras; Morita super-equivalences Citations:Zbl 1182.20006 PDFBibTeX XMLCite \textit{T. Khongsap} and \textit{W. Wang}, SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 012, 27 p. (2009; Zbl 1187.20002) Full Text: DOI arXiv EuDML