The diagonal derivative of a skew Schur polynomial

Darij Grinberg; Nazar Korniichuk; Kostiantyn Molokanov; Severyn Khomych

The diagonal derivative of a skew Schur polynomial

Combinatorics 2024-02-23 v1

Authors: Darij Grinberg , Nazar Korniichuk , Kostiantyn Molokanov , Severyn Khomych

Abstract

We prove a formula for the image of a skew Schur polynomial $s_{\lambda/\mu}\left( x_{1}, x_{2}, \ldots, x_{N}\right)$ under the differential operator $\nabla:= \dfrac{\partial}{\partial x_{1}} +\dfrac{\partial}{\partial x_{2}}+\cdots+\dfrac{\partial}{\partial x_{N}}$ . This generalizes a formula of Weigandt for $\nabla\left( s_{\lambda}\right)$ .

Keywords

skew schur polynomials diagonal derivative differential operator symmetric functions schur functions algebraic combinatorics

Cite

@article{arxiv.2402.14217,
  title  = {The diagonal derivative of a skew Schur polynomial},
  author = {Darij Grinberg and Nazar Korniichuk and Kostiantyn Molokanov and Severyn Khomych},
  journal= {arXiv preprint arXiv:2402.14217},
  year   = {2024}
}

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The diagonal derivative of a skew Schur polynomial

Abstract

Keywords

Cite

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