On a theorem of Barbara Schmid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

按检索

On a theorem of Barbara Schmid

Authors:	Larry Smith

Institution:	School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 - Mathematisches Institut der Universität, D 37073 Göttingen, Germany

Abstract:	Let be a finite group and $\rho\colon G\hookrightarrow\mathrm{GL} (n,\mathbb{C})$ a complex representation. Barbara Schmid has shown that the algebra of invariant polynomial functions $\mathbb{C}V]^G$ on the vector space $V=\mathbb{C}^n$ is generated by homogeneous polynomials of degree at most $\beta$ , where $\beta$ is the largest degree of a generator in a minimal generating set for $\mathbb{C}\mathrm{reg}_{\mathbb{C}}(G)]^G$ , and $\mathrm{reg}_{\mathbb{C}}(G)$ is the complex regular representation of . In this note we give a new proof of this result, and at the same time extend it to fields $\mathbb{F}$ whose characteristic is larger than , the order of the group .

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文