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When Polarizations Generate

Gerald W. Schwarz
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Abstract

Let G be a reductive complex algebraic group and V a finite-dimensional G-module. From elements of the invariant algebra C[V]^G we obtain by polarization elements of C[kV]^G, where k\geq 1 and kV denotes the direct sum of k copies of V. For G simple our main result is the classification of the G-modules V and integers k\geq 2 such that polarizations generate C[kV]^G.

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Gerald W. Schwarz. 2006-09-18. When Polarizations Generate. https://arxiv.org/abs/math/0609078

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