Abstract
This is a part of an ongoing project, the goal of which is to classify all semi-direct products \({\mathfrak {s}}={\mathfrak g}{\ltimes }V\) such that \({\mathfrak g}\) is a simple Lie algebra, V is a \({\mathfrak g}\)-module, and \({\mathfrak {s}}\) has a free algebra of symmetric invariants. In this paper, we obtain such a classification for the representations of the orthogonal and symplectic algebras.
Dedicated to A. Joseph on the occasion of his 75th birthday
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The first author is partially supported by the RFBR grant 
16-01-00818. The second author is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—project number 330450448.
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Panyushev, D.I., Yakimova, O.S. (2019). Semi-Direct Products Involving Sp2n or Spinn with Free Algebras of Symmetric Invariants. In: Gorelik, M., Hinich, V., Melnikov, A. (eds) Representations and Nilpotent Orbits of Lie Algebraic Systems. Progress in Mathematics, vol 330. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-23531-4_12
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