The citation from the June 2001 LMS Newsletter:

PROFESSOR J.A. (SANDY) GREEN is awarded the De Morgan Medal for his fundamental contributions to group representation theory. Green has been one of the most influential figures in representation theory of the last fifty years. In a 1955 paper Green startled the world of representation theory by giving the complex character table of GL(n, q) in all generality. This was completely unexpected in view of the very partial information available prior to his work.

Green then turned to the modular representation theory of finite groups. He established the now fundamental Green correspondence and his work provided the impetus for focussing attention on modules, in contrast to Brauer's original character theoretic approach. In particular, his work laid the foundations for the cyclic defect theory and for the categorical representation theory that has been at the centre of much of the most recent activity in this area.

His emphasis then changed to algebraic groups. His 1981 Springer volume on polynomial representations of general linear groups has been enormously influential while in recent years he has made fundamental contributions to the Hall algebra approach to quantum groups. Green has written key papers on many other topics, including the converse to Brauer's induction theorem and modular representations of groups of Lie type, and has introduced the concepts of Mackey functors, the Green ring, and G-algebras.

It is internationally agreed that Green is one of those who have most shaped modern representation theory, and he enjoys widespread respect and affection. It is especially fitting that this recognition of his work is given in the year that sees both the centenary of Brauer's birth and his own 75th birthday.