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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

   
 
 

 

Symmetric invariants related to representations of exceptional simple groups


Authors: Dmitri I. Panyushev and Oksana S. Yakimova
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 78 (2017), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2017, 161-170
MSC (2010): Primary 14L30, 17B08, 17B20, 22E46
DOI: https://doi.org/10.1090/mosc/261
Published electronically: December 1, 2017
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Dmitri I. Panyushev
Affiliation: Institute for Information Transmission Problems of the R.A.S, Moscow, Russia
Email: panyushev@iitp.ru

Oksana S. Yakimova
Affiliation: Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Deutschland
Email: oksana.yakimova@uni-jena.de

DOI: https://doi.org/10.1090/mosc/261
Keywords: Index of Lie algebra, coadjoint representation, symmetric invariants
Published electronically: December 1, 2017
Additional Notes: The research of the first author was carried out at the IITP RAS at the expense of the Russian Foundation for Sciences (project \N14–50–00150). The second author was partially supported by Graduiertenkolleg GRK 1523 “Quanten- und Gravitationsfelder”.
Dedicated: To our teacher Ernest B.Vinberg on occasion of his 80th birthday
Article copyright: © Copyright 2017 D.I.Panyushev, O.S.Yakimova

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