uniquely by certain vanishing and symmetry properties.

    We further show that the top homogeneous parts of the eigenvalue polynomials $c_{\lambda }$ coincide with the spherical polynomials $d_{\lambda }$, which arise as radial parts of $\g k$-spherical vectors of finite dimensional $\g g$-modules, and which are super-analogues of Jack polynomials. This generalizes results of Knop and Sahi [@KnopSahi].

    Finally, we make a precise connection between the polynomials $c_\lambda$ and the shifted super Jack polynomials of Sergeev and Veselov [@SerVes] for special values of the parameter. We show that the two families are related by a change of coordinates that we call the Frobenius transform.\
    *Keywords:* Lie superalgebras, the Capelli problem, super Jack polynomials, shifted super Jack polynomials.\
    *MSC2010:* 17B10, 05E05.
author:
- 'Siddhartha Sahi[^1] , Hadi Salmasian[^2]'
title: 'The Capelli problem for $\gl(m|n)$ and the spectrum of invariant differential operators'
---

Introduction
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One of the most celebrated results in classical invariant theory is the Capelli identity for $n\times n$ matrices. It plays a fundamental role in Hermann Weyl’s book [@Weyl]. The Capelli identity is profoundly connected to the representation theory of the Lie algebra $\gl(n)$. The well-known article of Roger Howe [@HoweRem] elucidated this connection by giving a conceptual proof 