Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra ?
Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra ?
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Zhedanov 的代数 AW(3) 和一阶情况下的双仿射 Hecke 代数。
DOI：
10.3842/sigma.2008.052
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发表时间：
2007
影响因子：
0.9
通讯作者：
T. Koornwinder
中科院分区：
文献类型：
--
作者：
T. Koornwinder
本文在作者前一篇文章的基础上，建立了Zhedanov代数AW（3）与对应于Askey-Wilson多项式的双仿射Hecke代数（DAHA）之间的关系。本文证明了这个DAHA的球面子代数与AW（3）同构，并附加了Casimir算子等于一个显式常数的关系。一个类似的结果与q-移位参数保持反球子代数。最后，作为球面子代数和反球面子代数特征的推论，证明了所考虑代数的中心化子和中心的一些定理。
This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) corre- sponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW(3) with an additional relation that the Casimir operator equals an explicit constant. A similar result with q-shifted parameters holds for the antispherical subalgebra. Some theorems on centralizers and centers for the algebras under consideration will finally be proved as corollaries of the characterization of the spherical and antispherical subalgebra.