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Typical separating invariants

M. Domokos
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Abstract

It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial invariants, then they can be separated by invariants depending only on at most $2\dim(V)$ variables of type $V$; when $G$ is reductive, invariants depending only on at most $\dim(V)+1$ variables suffice. Similar result is valid for rational invariants. Explicit bounds on the number of type $V$ variables in a typical system of separating invariants are given for the binary polyhedral groups, and this is applied to the invariant theory of binary forms.

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M. Domokos. 2005-11-11. Typical separating invariants. https://arxiv.org/abs/math/0511300

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