Homomorphisms between symplectic groups
Let \(F\) and \(F_ 1\) be fields with \(| F| > 5\), and \(n\), \(n_ 1\) be positive integers with \(n \geq n_ 1\). The authors study the homomorphisms between the symplectic groups \(Sp_{2n}(F)\) and \(Sp_{2n_ 1}(F_ 1)\). It is proved that there exists a non-trivial homomorphism from \(Sp_{2n}(F)\) to \(Sp_{2n_ 1}(F_ 1)\) if and only if \(n = n_ 1\), and there exists a non-trivial homomorphism from \(F\) to \(F_ 1\). It is also proved that almost all non-trivial homomorphisms from \(Sp_{2n}(F)\) to \(Sp_{2n}(F_ 1)\) are of standard type except \(n = 2\) and \(\text{char }F = \text{char }F_ 1 = 2\) in which case there may exist a class of ``exceptional'' non-trivial homomorphisms whose forms are given.
scientific article; zbMATH DE number 495842