Transvection free groups and invariants of polynomial tensor exterior algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Transvection free groups and invariants of polynomial tensor exterior algebras

Authors:	J Hartmann

Institution:	(1) IWR, Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg

Abstract:	Let :GGl(n, $\mathbb{F}$ ) be a representation of a finite groupG over a field $\mathbb{F}$ such that the ring of invariants $\mathbb{F}\left V \right]^G$ is a polynomial algebra $\mathbb{F}\left {f_1 ,... ,f_n } \right]$ . It is known that in the nonmodular case (i.e., when the order of the group is not divisible by the characteristic of $\mathbb{F}$ ), the invariants ofG acting on the tensor product $\mathbb{F}\left V \right] \otimes E\left V \right]$ of a polynomial and an exterior algebra are given by $\mathbb{F}\left {f_1 ,... ,f_n } \right] \otimes E\left {df_1 ,... ,df_n } \right]$ ,d denoting the exterior derivative. We show that in the modular case, the ring of invariants in $\mathbb{F}\left V \right] \otimes E\left V \right]$ is of this form if and only if $\mathbb{F}\left V \right]^G$ is a polynomial algebra and all pseudoreflections in (G) are diagonalizable.

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