Polarization of separating invariants

J. Draisma, G. Kemper, D.L. Wehlau

Research output: Contribution to journalArticleAcademicpeer-review

26 Citations (Scopus)

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 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.
Original languageEnglish
Pages (from-to)556-571
JournalCanadian Journal of Mathematics / Journal Canadien de Mathématiques
Volume60
Issue number3
DOIs
Publication statusPublished - 2008

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