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Polarization of Separating Invariants

Published online by Cambridge University Press:  20 November 2018

Jan Draisma ,
Gregor Kemper  and
David Wehlau
Jan Draisma
Affiliation:
Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands e-mail:, jdraisma@win.tue.nl
Gregor Kemper
Affiliation:
Technische Universität München, Zentrum Mathematik - M11, 85 748 Garching, Germany e-mail:, kemper@ma.tum.de
David Wehlau
Affiliation:
Department of Mathematics and Computer Science, Royal Military College, Kingston, ON, K7K 7B4 e-mail:, wehlau@rmc.ca
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Abstract

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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.

Keywords

13A5014K24
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 3 , 01 June 2008 , pp. 556 - 571
Copyright
Copyright © Canadian Mathematical Society 2008

References

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