James Alexander "Sandy" Green FRS (26 February 1926 – 7 April 2014) was a mathematician and Professor at the Mathematics Institute at the

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

, who worked in the field of

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

Early life

Sandy Green was born in February 1926 in

Rochester Rochester may refer to: Places Australia * Rochester, Victoria Canada * Rochester, Alberta United Kingdom *Rochester, Kent ** City of Rochester-upon-Medway (1982–1998), district council area ** History of Rochester, Kent ** HM Prison ...

New York New York most commonly refers to: * New York City, the most populous city in the United States, located in the state of New York * New York (state), a state in the northeastern United States New York may also refer to: Film and television * '' ...

, but moved to

Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the ancho ...

with his emigrant Scottish parents later that year. The family returned to Britain in May 1935 when his father, Frederick C. Green, took up the Drapers Professorship of French at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

Education

Green was educated at

the Perse School (He who does things for others does them for himself) , established = , closed = , type = Public schoolIndependent day school , religion = Nondenominational Christian , president = , head_label = Head , he ...

, Cambridge. He won a scholarship to the

University of St Andrews (Aien aristeuein) , motto_lang = grc , mottoeng = Ever to ExcelorEver to be the Best , established = , type = Public research university Ancient university , endowment ...

and matriculated aged 16 in 1942. He took an ordinary BSc in 1944, and then, after scientific service in the war, was awarded a BSc Honours in 1947. He gained his PhD at

St John's College, Cambridge St John's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge founded by the House of Tudor, Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corpo ...

in 1951, under the supervision of

Philip Hall Philip Hall FRS (11 April 1904 – 30 December 1982), was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups. Biography He was educated first at Christ's Hospital, where he won the Thomps ...

and

David Rees David or Dai Rees may refer to: Entertainment * David Rees (author) (1936–1993), British children's author * Dave Rees (born 1969), American drummer for SNFU and Wheat Chiefs * David Rees (cartoonist) (born 1972), American cartoonist and televis ...

Career

World War II

In the summer of 1944, he was conscripted for national scientific service at the age of eighteen, and was he was assigned to work at

Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...

, where he acted as a human "computer" carrying out calculations in Hut F, the "Newmanry", a department led by

Max Newman Maxwell Herman Alexander Newman, FRS, (7 February 1897 – 22 February 1984), generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operatio ...

, which used special-purpose Colossus computers to assist in breaking German naval codes.

Academic work

His first lecturing post (1950) was at the

University of Manchester , mottoeng = Knowledge, Wisdom, Humanity , established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Univer ...

, where Newman was his Head of Department. In 1964 he became a Reader at the

University of Sussex , mottoeng = Be Still and Know , established = , type = Public research university , endowment = £14.4 million (2020) , budget = £319.6 million (2019–20) , chancellor = Sanjeev Bhaskar , vice_chancellor = Sasha Roseneil , ...

, and then in 1965 was appointed as a Professor at the newly formed Mathematics Institute at

Warwick University , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (2020� ...

, where he led the algebra group. He spent several periods as a visiting academic in the United States, beginning with a year at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

in 1960–61, as well as similar visits to universities in France, Germany and Portugal. After retiring from Warwick he became a member of the faculty and Professor Emeritus at the Mathematics Institute of the University of Oxford, in whose meetings he participated actively. His final publication was produced at the age of eighty.

Work in mathematics

Green found all the

character Character or Characters may refer to: Arts, entertainment, and media Literature * ''Character'' (novel), a 1936 Dutch novel by Ferdinand Bordewijk * ''Characters'' (Theophrastus), a classical Greek set of character sketches attributed to The ...

s of

general linear group In mathematics, the general linear group of degree ''n'' is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, ...

s over

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...

s (Green 1955) and invented the Green correspondence in

modular representation theory Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field ''K'' of positive characteristic ''p'', necessarily a prime number. As well as ...

. Both Green functions in the

groups of Lie type In mathematics, specifically in group theory, the phrase ''group of Lie type'' usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phras ...

and

Green's relations In mathematics, Green's relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate. The relations are named for James Alexander Green, who introduced them in a paper of 1951. ...

in the area of

semigroup In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', ...

s are named after him. His final publication (2007) was a revised and augmented edition of his 1980 work, ''Polynomial Representations of GL(n)''.

Personal life

Green met his wife, Margaret Lord, at Bletchley Park, where she worked as a Colossus operator, also in the Newmanry section (Hut F). The couple married in August 1950, and have two daughters and a son. Up to his death, he lived in

Oxford Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

Honours

He was elected to the

Royal Society of Edinburgh The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

in 1968 and the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

in 1987 and was awarded two

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

prizes: the

Senior Berwick Prize The Berwick Prize and Senior Berwick Prize are two prizes of the London Mathematical Society awarded in alternating years in memory of William Edward Hodgson Berwick, a previous Vice-President of the LMS. Berwick left some money to be given to the s ...

in 1984 and the

de Morgan Medal The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society. The Society's most prestigious award, it is given in memory of Augustus De Morgan, who was the first President of the societ ...

in 2001.

Bibliography

* (1955
''The characters of the finite general linear group''
Trans. A. M. S. 80 402–447. * (2007
''Polynomial Representations of GL_n''
Lecture Notes in Mathematics, Springer, Vol. 830. 2nd edition with an ''Appendix on Schensted Correspondence and Littelmann Paths'', K. Erdmann, J. A. Green and M. Shocker

References

External links

* *
Warwick page Profile at Warwick University
{{DEFAULTSORT:Green, James Alexander 1926 births 2014 deaths Academics of the Victoria University of Manchester Academics of the University of Sussex Academics of the University of Warwick Alumni of St John's College, Cambridge Alumni of the University of St Andrews 20th-century British mathematicians 21st-century British mathematicians British science writers Fellows of the Royal Society Group theorists Bletchley Park people People from Oxford People educated at The Perse School