On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields

Details On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields

2009-11-02

arxiv.org/abs/0911.0379v3

Mathematics

Group Theory

Scientific paper

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

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