Symmetric invariants related to representations of exceptional simple groups

Panyushev, Dmitri; Yakimova, Oksana

doi:10.1090/mosc/261

Symmetric invariants related to representations of exceptional simple groups
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by Dmitri I. Panyushev and Oksana S. Yakimova

Trans. Moscow Math. Soc. 2017, 161-170

DOI: https://doi.org/10.1090/mosc/261

Published electronically: December 1, 2017

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Abstract:

We classify the finite-dimensional rational representations $V$ of the exceptional algebraic groups $G$ with ${\mathfrak {g}}=\mathsf {Lie } G$ such that the symmetric invariants of the semi-direct product ${\mathfrak {g}}\ltimes V\!$, where $V$ is an Abelian ideal, form a polynomial ring.

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