James E. Humphreys

James Edward Humphreys (* 1939 in Erie (Pennsylvania) ) is an American mathematician who deals with algebraic groups , Lie groups and Lie algebras and their representation theory.

Humphreys attended school in Erie (Pennsylvania) and studied at Oberlin College (Bachelor 1961) and from 1961 philosophy and mathematics at Cornell University . In 1964 he made his master's degree from Yale University , where he received his doctorate in 1966 under George B. Seligman ( Algebraic Lie Algebras over fields of prime characteristic ). In 1966 he became an Assistant Professor at the University of Oregon and in 1970 an Associate Professor at New York University . In 1974 he became an Associate Professor and in 1976 Professor at the University of Massachusetts . In 2003 he retired. In 1968/68 and 1977 he was at the Institute for Advanced Study , 1969/70 at the Courant Institute of Mathematical Sciences of New York University and 1985 visiting professor at Rutgers University .

He is known from various textbooks, including Lie algebras and their representations.

In 1976 he received the Lester Randolph Ford Award .

Fonts

• Arithmetic Groups, Lecture Notes in Mathematics 789, Springer Verlag 1980 (Lectures at the Courant Institute 1971)
• Conjugacy classes in semisimple algebraic groups, AMS 1995
• Introduction to Lie Algebras and Representation Theory, Springer Verlag, Graduate Texts in Mathematics, 1972, 7th edition 1997 (also translated into Chinese and Russian)
• Linear Algebraic Groups, Graduate Texts in Mathematics, Springer Verlag 1974, 1998 (also translated into Russian)
• Ordinary and modular representations of Chevalley groups, Springer Verlag 1976
• Modular representations of finite groups of Lie type, London Mathematical Society Lecture Note Series 326, Cambridge University Press 2006
• Reflection groups and Coxeter Groups, Cambridge University Press 1990
• Representations of semisimple Lie algebras in the BGG category O, AMS 2008
• Modular representations of simple Lie algebras, Bull. Amer. Math. Soc. (NS), Volume 35, 1998, pp. 105-122.
• Modular representations of classical Lie algebras, Bull. Amer. Math. Soc., Vol. 76, 1970, 878-882
• Algebraic groups and modular Lie algebras, Memoirs AMS 71, 1967
• Hilbert's fourteenth problem, Amer. Math. Monthly, Vol. 85, 1978, 341-353
• Representations of SL (2, p), Amer. Math. Monthly, Vol. 82, 1975, 21-39
• Highest weight modules for semisimple Lie algebras, in: Representation Theory I, Lecture Notes in Mathematics 831, Springer Verlag 1980, pp. 72-103

Web links

• Homepage

Individual evidence

1. ↑ Dates of birth according to the membership book of the Institute for Advanced Study 1980
2. ↑ James E. Humphreys in the Mathematics Genealogy Project (English)
3. ↑ For Representations of SL (2, p) , Amer. Math. Monthly 82: 21-39 (1975)