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

2008/10/31 by Ta Khongsap, Weiqiang Wang · 1 citation
Chemistry · Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #math.QA #math.RT

paper · pdf · doi:10.3842/sigma.2009.012

published as SIGMA 5 (2009), 012, 27 pages

arxiv created 2009/01/28 · openalex publication_date 2009/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Differential-difference operators associated to reflection groups

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