Quantum zonal spherical functions and Macdonald polynomials
Quantum zonal spherical functions and Macdonald polynomials
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DOI：
10.1016/j.aim.2003.11.007
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发表时间：
2002-10
影响因子：
1.7
通讯作者：
G. Letzter
中科院分区：
文献类型：
--
作者：
G. Letzter
将量子对称对的统一理论应用于q-特殊函数。前人的工作刻画了量子包络代数中的某些左余理想子代数，并建立了量子带状球函数的适当框架。在这里一个杰出的家庭这样的功能，不变下的Weyl群相关联的限制根，是一个家庭的麦克唐纳多项式，如图所示的Koornwinder和麦克唐纳。我们的结果将经典型李代数的早期工作放在一般的背景下，并扩展到例外情况。
A unified theory of quantum symmetric pairs is applied to q-special functions. Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions. Here a distinguished family of such functions, invariant under the Weyl group associated to the restricted roots, is shown to be a family of Macdonald polynomials, as conjectured by Koornwinder and Macdonald. Our results place earlier work for Lie algebras of classical type in a general context and extend to the exceptional cases.