We consider two natural gradings on the space of symmetric functions: by degree and by length. We introduce a differential operator T that leaves the components of this double grading invariant and exhibit a basis of bihomogeneous symmetric functions in which this operator is triangular. This allows us to compute the eigenvalues of T, which turn out to be nonnegative integers.

中文翻译：

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双齐次对称函数

我们考虑对称函数空间上的两种自然分级：按度数和按长度。我们引入了一个微分算子T，它保留了这个双分级不变量的分量，并展示了一个双齐对称函数的基础，其中这个算子是三角形的。这允许我们计算T的特征值，结果是非负整数。