Modular Vector Invariants of Cyclic Permutation Representations

Canadian mathematical bulletin

关键词: polynomial invariants of finite groups;   

DOI  :  10.4153/CMB-1999-014-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Vector invariants of finite groups (see the introduction for anexplanation of the terminology) have often been used to illustrate thedifficulties of invariant theory in the modular case: see,eg., cite{Ber}, cite{norway}, cite{fossum}, cite{MmeB},cite{poly} and cite{survey}. It is therefore all the moresurprising that the {it unpleasant} properties of these invariantsmay be derived from two unexpected, and remarkable, {it nice}properties: namely for vector permutation invariants of the cyclicgroup $mathbb{Z}/p$ of prime order in characteristic $p$ theimage of the transfer homomorphism $Tr^{mathbb{Z}/p} colonmathbb{F}[V] lra mathbb{F}[V]^{mathbb{Z}/p}$ is a prime ideal,and the quotient algebra $mathbb{F}[V]^{mathbb{Z}/p}/ Im(Tr^{mathbb{Z}/p})$ is a polynomial algebra on the top Chernclasses of the action.

【 授权许可】

Unknown