James Alexander Green. 26 February 1926—7 April 2014. (14th December 2019) - Donkin, Stephen; Erdmann, Karin
Abstract : James Alexander Green, known as Sandy, was a mathematician of great influence and distinction. He was an algebraist, famous for his work on modular representations of finite groups, and the development of the theory of polynomial representations of general linear groups. He was elected Fellow of the Royal Society of Edinburgh (1968) and Fellow of the Royal Society of London (1987). He was awarded prizes of the London Mathematical Society, a Senior Berwick Prize (in 1984) and the De Morgan Medal (in 2001). In his doctoral thesis, on semigroups, Sandy introduced fundamental relations, now known as 'Green's relations'. He determined the characters of arbitrary finite general linear groups published 1955. Sandy then turned to representations of finite groups over fields of prime characteristic; his work laid the foundations for the module theoretic approach to the subject. His next highlight is his monograph on polynomial representations of GL n, published in 1980, which has become the basis for algebraic highest weight theory. Furthermore, in 1995 he proved a fundamental result on Hall algebras, establishing a connection between quantum groups and representations of finite-dimensional quiver algebras.