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On rings of invariants of non-modular Abelian groups

Published online by Cambridge University Press:  17 April 2009

H.E.A. Campbell ,
J.C. Harris  and
D.L. Wehlau
H.E.A. Campbell
Affiliation:
Department of Mathematics and StatisticsQueen's UniversityKingston, Ontario, Canada, K7L 3N6 e-mail: [email protected]
J.C. Harris
Affiliation:
Department of MathematicsUniversity of TorontoToronto, OntarioCanadaM5S 1A1 e-mail: [email protected]
D.L. Wehlau
Affiliation:
Department of Mathematics and Computer ScienceRoyal Military CollegeKingston, OntarioCanadaM5S 1A1 and Department of Mathematics and StatisticsQueen's UniversityKingston, OntarioCanada K7L 3N6 e-mail: [email protected]
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We study the ring of invariant Laurent polynomials associated to the action of a finite diagonal group G on the symmetric algebra of a vector space over a field F. Here the characteristic p of the field F necessarily does not divide the order q = |G| of the group, so G is said to be non-modular. For certain representations of such groups, we can characterise generators of the ring of invariant polynomials in the original symmetric algebra, extending results of Campbell, Hughes, Pappalardi and Selick. In particular we obtain a recursive formula for the number of minimal generators for these rings of invariants.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 509 - 520
Copyright
Copyright © Australian Mathematical Society 1999

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