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arXiv · 1407.1878

Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials

Alexey Bolsinov·Anton Izosimov·Ivan Kozlov
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Abstract

For an arbitrary representation $\rho$ of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan-Kronecker invariants of $\rho$. Among other interesting properties, these numbers provide lower bounds for degrees of polynomial invariants of $\rho$. Furthermore, we prove that these lower bounds are exact if and only if the invariants are independent outside of a set of large codimension. Finally, we show that under certain additional assumptions our bounds are exact if and only if the algebra of invariants is freely generated.

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BibTeXRIS

Alexey Bolsinov, Anton Izosimov, Ivan Kozlov. 2014-07-07. Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials. https://arxiv.org/abs/1407.1878

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