When Polarizations Generate

Details When Polarizations Generate When Polarizations Generate

2006-09-03

arxiv.org/abs/math/0609078v3

Mathematics

Representation Theory

More general results, proofs improved, references added

Scientific paper

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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