On polarizations in invariant theory

Losik, Mark; Michor, Peter W.; Popov, Vladimir L.

On polarizations in invariant theory

Authors

Losik, Mark

Michor, Peter W.

Popov, Vladimir L.

Description

Given a reductive algebraic group $G$ and a finite dimensional algebraic $G$-module $V$, we study how close is the algebra of $G$-invariant polynomials on $V^{\oplus n}$ to the subalgebra generated by polarizations of $G$-invariant polynomials on $V$. We address this problem in a more general setting of $G$-actions on arbitrary affine varieties.
15 pages