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arXiv · 2001.08046

On Schur problem and Kostka numbers

Robert Coquereaux·Jean-Bernard Zuber
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Abstract

We reconsider the two related problems: distribution of the diagonal elements of a Hermitian n x n matrix of known eigenvalues (Schur) and determination of multiplicities of weights in a given irreducible representation of SU(n) (Kostka). It is well known that the former yields a semi-classical picture of the latter. We present explicit expressions for low values of n that complement those given in the literature, recall some exact (non asymptotic) relation between the two problems, comment on the limiting procedure whereby Kostka numbers are obtained from Littlewood-Richardson coefficients, and finally extend these considerations to the case of the B2 algebra, with a few novel conjectures.

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BibTeXRIS

Robert Coquereaux, Jean-Bernard Zuber. 2020-01-22. On Schur problem and Kostka numbers. https://arxiv.org/abs/2001.08046

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