Homomorphisms of unitary groups (Q5895412)

In problem XVII from \textit{D. James} et al [Commun. Algebra 9, 95-114 (1981; Zbl 0452.20045)] \textit{B. Weisfeiler} proposes a general formulation for homomorphisms between classical groups in terms of a congruence subgroup coming from an induced integral structure in the group. This formulation provides a good foundation for extending the fairly well understood situation for isomorphisms, though not all homomorphisms arise in this manner. The author of this paper establishes Weisfeiler's conjecture for homomorphisms between unitary groups over division rings which do not kill involutions. The central new idea involves moving subspaces in a controlled manner, intersecting them and counting dimensions. [Editor's comment: This paper is a word by word copy of the paper by \textit{D. G. James}, `Homomorphisms of unitary groups' in Math. Z. 178, No.3, 343-352 (1981; Zbl 0461.20022)]