Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
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DOI：
10.3842/sigma.2009.012
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发表时间：
2008-10
影响因子：
0.9
通讯作者：
Ta Khongsap;Weiqiang Wang
中科院分区：
文献类型：
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作者：
Ta Khongsap;Weiqiang Wang
引入了一个由经典Weyl群W生成的奇双仿射Hecke代数（DaHa）和两个反交换生成子的斜多项式子代数。证明该代数与另一个由W和两个多项式clifford子代数生成的新DaHa是Morita等价的。还有第三种代数包含一个自旋Weyl群代数，它与上述两个代数是森田（超）等价的。我们建立了这些代数的PBW性质，并通过Dunkl算子构造了verma型表示。
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.