Decomposition of symplectic matrices into products of commutators of symplectic involutions

摘要

A matrix A is symplectic if where A symplectic matrix A is a commutator of symplectic involutions if where X and Y are symplectic and In this article, we prove that every complex symplectic matrix of size greater than 2 can be decomposed into a product of at most three commutators of involutions. Communicated by Miriam Cohen