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Modular Vector Invariants of Cyclic Permutation Representations

Published online by Cambridge University Press:  20 November 2018

Larry Smith
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Abstract

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Vector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, e.g., [1], [2], [4], [7], [11] and [12]. It is therefore all the more surprising that the unpleasant properties of these invariants may be derived from two unexpected, and remarkable, nice properties: namely for vector permutation invariants of the cyclic group $Z/p$ of prime order in characteristic $p$ the image of the transfer homomorphism $\text{T}{{\text{r}}^{Z/p}}\,:\,F[V]\,\to \,F{{[V]}^{Z/p}}$ is a prime ideal, and the quotient algebra $F{{[V]}^{Z/p}}/\,\text{IM(T}{{\text{r}}^{Z/p}})$ is a polynomial algebra on the top Chern classes of the action.

Keywords

13A50polynomial invariants of finite groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 1 , 01 March 1999 , pp. 125 - 128
Copyright
Copyright © Canadian Mathematical Society 1999

References

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