对称函数算子的q-类
q-Analogs of symmetric function operators
摘要：
对于对称函数空间上的任何同态V，我们引入了一个操作，它创建了一个Q-模拟的V.通过给出几个例子，我们证明了这种量子化自然发生在对称函数的理论。特别是，我们表明，霍尔-Littlewood对称函数形成采取这种q模拟的舒尔对称函数和麦克唐纳对称函数出现采取的q模拟的霍尔-Littlewood对称函数的参数t。这个关系，然后用来推导递归的麦克唐纳q，t-Kostka系数。
英文摘要：
For any homomorphism V on the space of symmetric functions, we introduce an operation which creates a q-analog of V. By giving several examples we demonstrate that this quantization occurs naturally within the theory of symmetric functions. In particular, we show that the Hall-Littlewood symmetric functions are formed by taking this q-analog of the Schur symmetric functions and the Macdonald symmetric functions appear by taking the q-analog of the Hall-Littlewood symmetric functions in the parameter t. This relation is then used to derive recurrences on the Macdonald q,t-Kostka coefficients.
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