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Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
Інший ID:
2000 Mathematics Subject Classification: 20C08
Посилання:
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type / T. Khongsap, W. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 17 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. This research is partially supported by NSF grant DMS-0800280. The main results of this paper for type A were obtained at MSRI in 2006.
Дата:
2009
Переглядів:
377
Завантажень:
235
Анотація:
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.
