James Alexander Green

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James Alexander Green (born February 26, 1926 in Rochester , New York , † April 7, 2014 in Oxford , Oxfordshire ) was a British mathematician who dealt with the representation theory of groups.

Green had Scottish ancestry and the family moved back to Great Britain via Toronto in 1934, where Green's father was a French professor at Cambridge. Green studied at the University of St. Andrews and Cambridge University (St. Johns College), where he received his doctorate in 1951 under Philip Hall . During World War II he worked on the Enigma deciphering project in Bletchley Park . There he met his future wife, whom he married 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 completely determined the characters of the general linear group over finite fields (The Characters of the finite general linear group, Transactions American Mathematical Society, Vol. 80, 1955, p. 402). Various 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 the Lie type . He developed the categorical and axiomatic group theory and made important contributions to the polynomial representation theory of the general linear group and related to the investigation of Schur's 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 the De Morgan Medal of the London Mathematical Society in 2001 and the Senior Berwick Prize in 1984 .

Fonts

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

Individual evidence

  1. ↑ The Royal Society regrets to announce the deaths of the following Fellows in 2014.Retrieved from royalsociety.org on April 9, 2014

Web links

personal data
SURNAME Green, James Alexander
ALTERNATIVE NAMES Green, Sandy
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH February 26, 1926
PLACE OF BIRTH Rochester (New York) , United States
DATE OF DEATH April 7, 2014
Place of death Oxford , UK