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arXiv · 1905.01414

Highest weight vectors in plethysms

Kazufumi Kimoto·Soo Teck Lee
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Abstract

We realize the $\mathrm{GL}_n(\mathbb{C})$-modules $S^k(S^m(\mathbb{C}^n))$ and $\Lambda^k(S^m(\mathbb{C}^n))$ as spaces of polynomial functions on $n\times k$ matrices. In the case $k=3$, we describe explicitly all the $\mathrm{GL}_n(\mathbb{C})$-highest weight vectors which occur in $S^3(S^m(\mathbb{C}^n))$ and in $\Lambda^3(S^m(\mathbb{C}^n))$ respectively.

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BibTeXRIS

Kazufumi Kimoto, Soo Teck Lee. 2019-05-04. Highest weight vectors in plethysms. https://doi.org/10.1007/s00220-019-03639-6

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