James E. Humphreys

James Edward Humphreys (1939, Erie, Pennsylvania) is an American mathematician, who works on algebraic groups, Lie groups, and Lie algebras and applications of these mathematical structures. He is known as the author of several mathematical texts, especially Introduction to Lie Algebras and Representation Theory.[1]

Early life and education

Humphreys attended elementary and secondary school in Erie, Pennsylvania and then studied at Oberlin College (bachelor's degree 1961) and from 1961 philosophy and mathematics at Cornell University. At Yale University he earned his master's degree in 1964 and his PhD in 1966 under George B. Seligman with thesis Algebraic Lie Algebras over fields of prime characteristic.[2]

Career

In 1966 he became an assistant professor at the University of Oregon and in 1970 an associate professor at New York University. At the University of Massachusetts Amherst he became in 1974 an associate professor and in 1976 a full professor; in 2003 he retired there as professor emeritus. In 1968/69 and in 1977 he was a visiting scholar at the Institute for Advanced Study[3] and in 1969/70 at the Courant Institute of Mathematical Sciences of New York University. In 1985 he was a visiting professor at Rutgers University.

Awards

In 1976 he received the Lester R. Ford Award for the publication Representations of SL(2,p).[4]

Works

  • Arithmetic Groups, Lecture Notes in Mathematics 789, Springer Verlag 1980 (from lectures at the Courant Institute 1971)
  • Conjugacy classes in semisimple algebraic groups, AMS 1995[5] MathSciNet data. MR 1343976
  • 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) MathSciNet data. MR 0396773
  • Ordinary and modular representations of Chevalley groups, Springer Verlag 1976 MathSciNet data. MR 0453884
  • Modular representations of finite groups of Lie type, London Mathematical Society Lecture Note Series 326, Cambridge University Press 2006[6]
  • Reflection Groups and Coxeter Groups, Cambridge University Press 1990 MathSciNet data. MR 1066460
  • Representations of semisimple Lie algebras in the BGG category O, AMS 2008[7]
  • Modular representations of simple Lie algebras, Bull. Amer. Math. Soc. (N.S.), Vol. 35, 1998, pp. 105–122. doi:10.1090/S0273-0979-98-00749-6
  • Modular representations of classical Lie algebras, Bull. Amer. Math. Soc., Vol. 76, 1970, 878–882 doi:10.1090/S0002-9904-1970-12594-0
  • 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 , 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 doi:10.1007/BFb0089779

References

  1. ↑ "Review: Introduction to Lie Algebras and Representation Theory". MAA Reviews. December 31, 2012.
  2. ↑ James E. Humphreys at the Mathematics Genealogy Project
  3. ↑ "Humphreys, James E." ias.edu. Retrieved 28 January 2015.
  4. ↑ "Representations of SL ". maa.org. Retrieved 28 January 2015.
  5. ↑ Procesi, Claudio (1997). "Review: Conjugacy classes in semisimple algebraic groups, by James E. Humphreys" (PDF). Bull. Amer. Math. Soc. (N.S.). 34 (1): 55–56. doi:10.1090/s0273-0979-97-00689-7.
  6. ↑ Benson, Dave (2007). "Review: Modular representations of finite groups of Lie type, by James E. Humphreys". SIAM Review. 49 (1): 129–131. doi:10.1137/SIREAD000049000001000123000001. JSTOR 20453917.
  7. ↑ Soergel, Wolfgang (2010). "Review: Representations of semisimple Lie algebras in the BGG category O, by James E. Humphreys". Bull. Amer. Math. Soc. (N.S.). 47 (2): 367–371. doi:10.1090/s0273-0979-09-01266-X.
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