James Alexander Green

James Alexander Green ( born 1926 in Rochester (New York)) is a British mathematician who deals with representation theory of groups.

Green has Scottish ancestors, the family moved over Toronto in 1934 after the UK, where Green's father was French professor in Cambridge. Green studied at the University of St. Andrews and Cambridge University (St. John's College ), where he earned his doctorate at Philip Hall, 1951. During the Second World War he worked on Enigma Entzifferungsprojekt at Bletchley Park, where he met his future wife (marriage in 1950 ). He was a lecturer at the University of Manchester, 1965 at the University of Sussex and from 1966 at the University of Warwick.

In 1955 he determined the characters of the general linear group over finite fields completely (The characters of the finite general linear group, Transactions American Mathematical Society, Bd.80, 1955, S.402 ). Different concepts in representation theory are named after him ( such as Green correspondence in the modular representation theory of finite groups, Green relations in semigroups and Green functions in the representation theory of finite groups of Lie type). He developed the categorical and axiomatic set theory and made ​​important contributions to the polynomial representation theory of the general linear group and related to the study of the Schur algebra. In the 1990s, he also examined the representations of quantum groups via a connection with Hall algebras.

In 1987 he became a member of the Royal Society. He received in 2001 the De Morgan Medal of the London Mathematical Society in 1984 and the Senior Berwick Prize.

Writings

  • Polynomial Representations of GL ( n ), Springer, Lecture Notes in Mathematics Bd.830, 1980, 2007
  • Lectures on modular representation theory of finite groups, Giessen, Institute of Mathematics, 1974
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