This article is cited in 3 papers

Symmetric invariants related to representations of exceptional simple groups

D. I. Panyushev^a, O. S. Yakimova<sup>b

a</sup> Institute for Information Transmission Problems of the R.A.S, Moscow, Russia
^b Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Deutschland

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.

Key words and phrases: index of Lie algebra, coadjoint representation, symmetric invariants.

UDC: 512.815.4, 512.745.2

MSC: 14L30, 17B08, 17B20, 22E46

Received: 30.03.2017
Revised: 30.04.2017

Language: English

 English version: Transactions of the Moscow Mathematical Society, 2017, 78, 161–170

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