Modular Vector Invariants of Cyclic Permutation Representations

Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 125-128

Résumé

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.

Détail

DOI : 10.4153/CMB-1999-014-5

Mots-clés : 13A50, polynomial invariants of finite groups