The diagonal derivative of a skew Schur polynomial

Abstract

We prove a formula for the image of a skew Schur polynomial $s_{\lambda /\mu }\left(x_1,x_2,\dots ,x_N\right)$ under the differential operator $\nabla :=\frac{\partial }{\partial x_1}+\frac{\partial }{\partial x_2}+\cdots +\frac{\partial }{\partial x_N}$. This generalizes a formula of Weigandt for $\nabla \left(s_{\lambda }\right)$.

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