POLARIZATIONS IN CLASSICAL INVARIANT THEORY

MARK LOSIK (UNIVERSITY OF SARATOV)

Abstract: We give a weak version of the first main theorem of invariant theory, namely, we describe a class of representations of a reductive algebraic group on a vector space V such that ℂ[V^{q}]^{G} is the integral closure of ℂ[V^{q}]_{pol}^{G}, the subring generated by all generalized polarizations, in ℂ[V^{q}]. For finite groups we have stronger results.