Sandy Green (mathematician)
{{Short description|British mathematician (1926–2014)}}
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{{Other people|James Green}}
{{EngvarB|date=August 2014}}
{{Use dmy dates|date=July 2020}}
{{Infobox scientist
| name = Sandy Green
| image = Sandy Green (mathematician).gif
| image_size =
| caption =
| birth_date = {{Birth date|df=yes|1926|02|26}}
| birth_place = Rochester, New York, US
| death_date = {{Death date and age|df=yes|2014|04|07|1926|02|26}}
| death_place =
| citizenship = British, American
| nationality =
| fields = Mathematics
| workplaces = Bletchley Park
| alma_mater = University of St Andrews
St John's College, Cambridge
| doctoral_advisor = Philip Hall, David Rees
| doctoral_students = Perdita Stevens
| known_for = Work on group representation theory, Green's relations
| author_abbrev_bot =
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| influences =
| influenced =
| awards = Senior Berwick Prize (1984)
de Morgan Medal (2001)
}}
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, who worked in the field of representation theory.
Early life
Sandy Green was born in February 1926 in Rochester, New York, but moved to Toronto 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.
Education
Green was educated at the Perse School, Cambridge. He won a scholarship to the University of St Andrews 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 in 1951, under the supervision of Philip Hall and David Rees.J. A. Green (1951) Abstract Algebra and Semigroups, PhD thesis, University of Cambridge{{citation | last=Green | first= James A. | title=On the structure of semigroups | zbl=0043.25601 | journal=Ann. Math. |series=2 | volume=54 | pages=163–172 | year=1951 | issue= 1 | doi=10.2307/1969317 | jstor= 1969317 | hdl= 10338.dmlcz/100067}}{{Citation | last2=Roseblade | first2=J. E. | last3=Thompson | first3=John G. |author3-link=John G. Thompson | last1=Green | first1=J. A. | title=Obituary: Philip Hall | doi=10.1112/blms/16.6.603 | mr=758133 | year=1984 | journal=The Bulletin of the London Mathematical Society | issn=0024-6093 | volume=16 | issue=6 | pages=603–626}}
Career
=World War II=
In the summer of 1944, he was conscripted for national scientific service at the age of eighteen, and was assigned to work at Bletchley Park, where he acted as a human "computer" carrying out calculations in Hut F, the "Newmanry", a department led by Max Newman, which used special-purpose Colossus computers to assist in breaking German naval codes.{{mactutor|id=Green_Sandy|title=James Alexander Green}}
=Academic work=
His first lecturing post (1950) was at the University of Manchester, where Newman was his Head of department. In 1964 he became a Reader at the University of Sussex, and then in 1965 was appointed as a professor at the newly formed Mathematics Institute at Warwick University, 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 in Princeton, New Jersey 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.
Work in mathematics
According to the Fields Medallist John G. Thompson,{{citation|author=Thompson, John G.|title=Vertices and sources|journal=Journal of Algebra|volume=6|issue=1|year=1967|pages=1–6|doi=10.1016/0021-8693(67)90009-9 |url=https://core.ac.uk/download/pdf/82813217.pdf}} Green showed, in two important papers,{{citation|doi=10.1007/BF01558601 |title=On the indecomposable representations of a finite group |date=1958 |last1=Green |first1=J. A. |journal=Mathematische Zeitschrift |volume=70 |pages=430–445 }}{{citation|doi=10.1007/BF01193108 |title=Blocks of modular representations |date=1962 |last1=Green |first1=J. A. |journal=Mathematische Zeitschrift |volume=79 |pages=100–115 }} that information about finite groups can be derived from knowledge about indecomposable modules of p-groups.
Green found all the characters of general linear groups over finite fields (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 semigroups 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
Honours
He was elected to the Royal Society of Edinburgh in 1968 and the Royal Society in 1987{{citation | url=http://newsletter.lms.ac.uk/09.html#78 | title=Obituaries: James Alexander (Sandy) Green | publisher=London Mathematical Society | accessdate=5 July 2014 | url-status=dead|archive-url=https://web.archive.org/web/20140714152127/http://newsletter.lms.ac.uk/09.html|archive-date=2014-07-14 }} and was awarded two London Mathematical Society prizes: the Senior Berwick Prize in 1984{{citation| url=http://www-groups.dcs.st-and.ac.uk/~history/Societies/LMSBerwick.html | title=Berwick prizes | publisher=The MacTutor History of Mathematics archive }} and the de Morgan Medal in 2001.{{citation | url=http://newsletter.lms.ac.uk/james-alexander-sandy-green-1926-2014/ | title=Citation for James Alexander Green | publisher=London Mathematical Society | accessdate=5 July 2014 }}{{citation|last1=Donkin|first1=Stephen|last2=Erdmann|first2=Karin|date=2019-12-30|title=James Alexander Green. 26 February 1926 – 7 April 2014|journal=Biographical Memoirs of Fellows of the Royal Society|volume=67|pages=173–190|doi=10.1098/rsbm.2019.0012|doi-access=free}}
Bibliography
- (1955) [https://www.jstor.org/stable/1992997 The characters of the finite general linear group], Trans. A. M. S. 80 402–447.
- (2007) [https://www.springer.com/west/home/new+%26+forthcoming+titles+%28default%29?SGWID=4-40356-22-173696918-0 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
- {{MathGenealogy|id=27130|title=James Alexander Green}}
- [https://web.archive.org/web/20080813025251/http://www2.warwick.ac.uk/fac/sci/maths/people/staff/sandy_green/ Warwick page Profile at Warwick University]
{{De Morgan Medallists}}
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{{DEFAULTSORT:Green, James Alexander}}
Category:Academics of the Victoria University of Manchester
Category:Academics of the University of Sussex
Category:Academics of the University of Warwick
Category:Alumni of St John's College, Cambridge
Category:Alumni of the University of St Andrews
Category:20th-century British mathematicians
Category:21st-century British mathematicians
Category:British science writers
Category:Fellows of the Royal Society