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Polarization of Separating Invariants

Published:2008-06-01
Printed: Jun 2008
• Jan Draisma
• Gregor Kemper
• David Wehlau
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Abstract

We prove a characteristic free version of Weyl's theorem on polarization. Our result is an exact analogue of Weyl's theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of \emph{cheap polarization}, and show that it is enough to take cheap polarizations of invariants of just one copy of a representation to obtain separating vector invariants for any number of copies. This leads to upper bounds on the number and degrees of separating vector invariants of finite groups.
 Keywords: Jan Draisma, Gregor Kemper, David Wehlau
 MSC Classifications: 13A50 - Actions of groups on commutative rings; invariant theory [See also 14L24] 14L24 - Geometric invariant theory [See also 13A50]