On the conjugacy classes in the orthogonal and symplectic groups over algebraically closed fields

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• 作者：Krishnendu Gongopadhyay
• 关键词：Orthogonal group ; Symplectic group ; Conjugacy classes
• 刊名：Expositiones Mathematicae
• 出版年：2010
• 出版时间：2010
• 年：2010
• 卷：28
• 期：4
• 页码：351-356
• 全文大小：150 K

文摘

Let be an algebraically closed field. Let be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B over . Suppose the characteristic of is sufficiently large, i.e. either zero or greater than the dimension of . Let denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in are conjugate if and only if they have the same elementary divisors.