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Hecke-Clifford algebras and spin Hecke algebras. IV: Odd double affine type. (English) Zbl 1187.20002

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).

MSC:

20C08 Hecke algebras and their representations
20F55 Reflection and Coxeter groups (group-theoretic aspects)

Citations:

Zbl 1182.20006
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