James Alexander Green
Encyclopedia
James Alexander "Sandy" Green FRS
(b. 1926) is a mathematician and retired Professor at the Mathematics Institute at the University of Warwick
, who is still active in the field of representation theory
.
James Alexander Green was born in 1926 in Rochester, New York, but moved to Toronto
with his emigrant Scottish
parents at a very early age. The family returned to Britain in 1934 when his father, Frederick C. Green, took up the Drapers Professorship of French
at the University of Cambridge
.
, Cambridge and his first degree was gained at the University of St Andrews
during the Second World War. He gained his Ph.D. at St John's College, Cambridge
in 1951, under the supervision of Philip Hall
.
, where he assisted in the Enigma project.
. In 1965 he moved to the University of Sussex
, and then in 1966 to Warwick University. He has spent several periods as a visiting academic in the United States, beginning with a year at the Institute for Advanced Study
in Princeton, New Jersey
in 1960-61, as well as similar visits to universities in France, Germany and Portugal.
s over finite field
s (Green 1955) and invented the Green correspondence in modular representation theory
. Both Green functions
in the representation theory
of groups of Lie type and Green's relations
in the area of semigroup
s are named after him. His most recent publication (2007) is a revised and augmented edition of his 1980 work, Polynomial Representations of GL(n).
.
in 1987 and was awarded the Senior Berwick Prize
in 1984 and the de Morgan Medal
in 2001.
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
(b. 1926) is a mathematician and retired Professor at the Mathematics Institute at the University of Warwick
University of Warwick
The University of Warwick is a public research university located in Coventry, United Kingdom...
, who is still active in the field of representation theory
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 studiesmodules over these abstract algebraic structures...
.
Early life
James Alexander Green was born in 1926 in Rochester, New York, but moved to Toronto
Toronto
Toronto is the provincial capital of Ontario and the largest city in Canada. It is located in Southern Ontario on the northwestern shore of Lake Ontario. A relatively modern city, Toronto's history dates back to the late-18th century, when its land was first purchased by the British monarchy from...
with his emigrant Scottish
Scottish people
The Scottish people , or Scots, are a nation and ethnic group native to Scotland. Historically they emerged from an amalgamation of the Picts and Gaels, incorporating neighbouring Britons to the south as well as invading Germanic peoples such as the Anglo-Saxons and the Norse.In modern use,...
parents at a very early age. The family returned to Britain in 1934 when his father, Frederick C. Green, took up the Drapers Professorship of French
Drapers Professor of French
The Drapers Professorship of French is the senior professorship in the study of the French language at the University of Cambridge, and was founded in 1919 by a donation from the Worshipful Company of Drapers.-Drapers Professors:...
at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
.
Education
Green was educated at the Perse SchoolThe Perse School
The Perse Upper School is an independent secondary co-educational day school in Cambridge, England. The school was founded in 1615 by Dr Stephen Perse, a Fellow of Gonville and Caius College, Cambridge, and has existed on several different sites in the city before its present home on Hills...
, Cambridge and his first degree was gained at the University of St Andrews
University of St Andrews
The University of St Andrews, informally referred to as "St Andrews", is the oldest university in Scotland and the third oldest in the English-speaking world after Oxford and Cambridge. The university is situated in the town of St Andrews, Fife, on the east coast of Scotland. It was founded between...
during the Second World War. He gained his Ph.D. at St John's College, Cambridge
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
in 1951, under the supervision of Philip Hall
Philip Hall
Philip Hall FRS , was an English mathematician.His major work was on group theory, notably on finite groups and solvable groups.-Biography:...
.
WWII
Towards the end of the war he was assigned to work at Bletchley ParkBletchley Park
Bletchley Park is an estate located in the town of Bletchley, in Buckinghamshire, England, which currently houses the National Museum of Computing...
, where he assisted in the Enigma project.
Academic work
His first lecturing post was at the University of ManchesterUniversity of Manchester
The University of Manchester is a public research university located in Manchester, United Kingdom. It is a "red brick" university and a member of the Russell Group of research-intensive British universities and the N8 Group...
. In 1965 he moved to the University of Sussex
University of Sussex
The University of Sussex is an English public research university situated next to the East Sussex village of Falmer, within the city of Brighton and Hove. The University received its Royal Charter in August 1961....
, and then in 1966 to Warwick University. He has spent several periods as a visiting academic in the United States, beginning with a year at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
in 1960-61, as well as similar visits to universities in France, Germany and Portugal.
Work in mathematics
Green found all the characters of general linear groupGeneral linear group
In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible...
s over finite field
Finite field
In abstract algebra, a finite field or Galois field is a field that contains a finite number of elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and coding theory...
s (Green 1955) and invented the Green correspondence in modular representation theory
Modular representation theory
Modular representation theory is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic...
. Both Green functions
Deligne–Lusztig theory
In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced by ....
in the representation theory
Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication...
of groups of Lie type and Green's relations
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
Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element...
s are named after him. His most recent publication (2007) is a revised and augmented edition of his 1980 work, Polynomial Representations of GL(n).
Personal life
Green met his wife, Margaret, during his time at Bletchley Park. The couple married in 1950, and have two daughters and a son. He now lives in OxfordOxford
The city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...
.
Honours
He was elected to the Royal SocietyRoyal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
in 1987 and was awarded the Senior Berwick Prize
Berwick Prizes
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 society to establish two prizes...
in 1984 and the de Morgan Medal
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 society....
in 2001.