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Invariant theory and Steenrod operations – maps between rings of invariants

Published online by Cambridge University Press:  24 October 2008

Zafer Mahmud  and
Larry Smith
Zafer Mahmud
Affiliation:
Department of Mathematics, University of Kuwait, Kuwait City, Kuwait e-mail: [email protected]
Larry Smith
Affiliation:
Mathematisches Institut der Universität, Bunsenstrasse 3–5, D 37073 Göttingen, Germany e-mail: [email protected]
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Abstract

Let G ′, G ″ be finite groups and p ′: G ↪ GL(n ′,ℚ), p ″: G ″ ↪ GL(n ″, ℚ) faithful rational representations. If T: V′ = ℚn′ → ℚn″ = V ″ is a linear transformation and Ξ: G ′ → G ″ a function such that

then there are induced algebra homomorphisms ℚ[V ″] → ℚ[V ] and ℚ[V ″]G ″ → ℚ[V ′]G ′ making the diagram

commute. In this note we isolate the invariant theory portion of [1] and extend it to provide a necessary and sufficient condition that an algebra homomorphism between rings of invariants ℚ[V ″]G ″ → ℚ[V ′]G ′ arises in this way.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 1 , July 1996 , pp. 103 - 116
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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