A generalized Macdonald operator
A generalized Macdonald operator
复制标题
广义麦克唐纳算子
DOI：
10.1093/imrn/rnq233
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
E. Emsiz
中科院分区：
文献类型：
--
作者：
J. F. van Diejen;E. Emsiz
我们提出了一个明确的差分算子对角化的麦克唐纳多项式与（任意）容许对不可约晶体学根系统。通过对偶对称性，这给出了一个明确的皮耶里公式的麦克唐纳多项式的问题。最简单的例子，我们的建设恢复麦克唐纳著名的差分算子和相关的皮耶里公式有关的极小和准极小的重量。作为进一步的副产品，显式的扩展和Littlewood-Richardson型公式得到的麦克唐纳多项式与一类特殊的小重量。
We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems. By the duality symmetry, this gives rise to an explicit Pieri formula for the Macdonald polynomials in question. The simplest examples of our construction recover Macdonald's celebrated difference operators and associated Pieri formulas pertaining to the minuscule and quasi-minuscule weights. As further by-products, explicit expansions and Littlewood-Richardson type formulas are obtained for the Macdonald polynomials associated with a special class of small weights.