We establish a positivity property for the difference of products of certain Schur functions, s λ (x), where λ varies over a fundamental Weyl chamber in ℝ n and x belongs to the positive orthant in ℝ n . Further, we generalize that result to the difference of certain products of arbitrary numbers of Schur functions. We also derive a log-convexity property of the generalized hypergeometric functions of two Hermitian matrix arguments, and we show how that result may be extended to derive higher-order log-convexity properties.
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机译：我们为某些Schur函数的乘积s λ（x）的差异建立了一个正性性质，其中λ在ℝ n 的基本Weyl腔中变化，x属于ℝ n 中的正正变体。此外，我们将该结果推广到任意数量的Schur函数的某些乘积之差。我们还导出了两个Hermitian矩阵自变量的广义超几何函数的对数凸性，并且我们展示了如何扩展该结果以导出高阶对数凸性。
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