turkmath.org

The symplectic group is a classical group defined as the set of linear transformations of an even dimensional vector space over a field which preserve a non-degenerate skew-symmetric bilinear form. In this talk, we present several simple maps generating the symplectic group. These types of maps might be called positive transvections based on Grove’s earlier work. Positive transvections are a very simple form of transvections and using those maps, we present easier proofs of various well-known theorems.