Thomas Jones Enright Explained

Thomas Jones Enright
Birth Date:	August 15, 1947
Birth Place:	Concord, New Hampshire, United States
Death Place:	San Diego, California, United States
Field:	Mathematics
Work Institutions:	UCSD
Alma Mater:	Harvard University B.S. & University of Washington Ph.D.
Doctoral Advisor:	Ramesh A. Gangolli
Prizes:	Alfred P. Sloan Research Fellowship

Thomas Jones Enright (August 15, 1947  - January 27, 2019) was an American mathematician known for his work in the algebraic theory of representations of real reductive Lie groups.

Biography

Enright received a B.S. from Harvard University in 1969 and a Ph.D. in 1973 from the University of Washington under the direction of Ramesh A. Gangolli. From 1973 to 1975 he was the Hedrick Assistant Professor in UCLA working with Veeravalli S. Varadarajan, and spent the 1976-1977 year after in the Institute for Advanced Study at Princeton, N. J. before starting at University of California at San Diego in 1977. He was chair of the mathematics department of UCSD from 1986 to 1990.^[1] In 2010 he retired due to symptoms of Parkinson's disease.

Contributions

In the mid-1970s, Enright introduced new methods that led him to an algebraic way of looking at discrete series (which were fundamental representations constructed by Harish-Chandra in the early 1960s), and to an algebraic proof of the Blattner multiplicity formula.

He was known for Enright–Varadarajan modules,^{[2] [3]} Enright resolutions, and the Enright completion functor,^{[4] [5] [6] [7]} which has had a lasting influence in algebra.

Recognition

• Recipient of Alfred P. Sloan Fellowship, 1978^[8]
• Enright's work was the subject of a Bourbaki Seminar by Michel Duflo^[9]

Bibliography

• Enright . Thomas J . 1979 . On the Fundamental Series of a Real Semisimple Lie Algebra: Their Irreducibility, Resolutions and Multiplicity Formulae . Annals of Mathematics . 110 . 1. 1–82 . 10.2307/1971244 . 1971244 .
• Enright . Thomas J. . Varadarajan . V. S. . 1975 . On an Infinitesimal Characterization of the Discrete Series . Annals of Mathematics . 102 . 1. 1–15 . 10.2307/1970970 . 1970970 .
• Enright, Thomas; Howe, Roger; Wallach, Nolan (1983-01-01). Trombi, P. C., ed. A Classification of Unitary Highest Weight Modules. Progress in Mathematics. Birkhäuser Boston. pp. 97–143. doi:10.1007/978-1-4684-6730-7_7. .
• Enright . T. J. . Wallach . N. R. . 1980 . Notes on homological algebra and representations of Lie algebras . Duke Mathematical Journal . 47 . 1. 1–15 . 10.1215/S0012-7094-80-04701-8 .
• Davidson . Mark G. . Enright . Thomas J. . Stanke . Ronald J. . 1991. Differential operators and highest weight representations . Memoirs of the American Mathematical Society . 94 . 455. 0 . 10.1090/memo/0455 .
• Enright, Thomas J.; Hunziker, Markus; Pruett, W. Andrew (2014-01-01). Howe, Roger; Hunziker, Markus; Willenbring, Jeb F., eds. Diagrams of Hermitian type, highest weight modules, and syzygies of determinantal varieties. Progress in Mathematics. Springer New York. pp. 121–184. doi:10.1007/978-1-4939-1590-3_6. .
• Enright . Thomas J . 1978 . On the algebraic construction and classification of Harish-Chandra modules . Proceedings of the National Academy of Sciences . 75 . 3. 1063–1065 . 10.1073/pnas.75.3.1063 . 16592507 . 411407 . 1978PNAS...75.1063E . free .

External links

• • Homepage of Thomas Jones Enright
• Thomas Jones Enright's obituary

Notes and References

1. Web site: UCSD Math Department History. Support. Math Computing. www.math.ucsd.edu. 2016-03-15.
2. Wallach. Nolan R.. 1976-01-01. On the Enright–Varadarajan modules: A construction of the discrete series. Annales Scientifiques de l'École Normale Supérieure . Série 4. en. 9. 81–101. 0012-9593. 10.24033/asens.1304. free.
3. Web site: Parthasarathy: A generalization of the Enright–Varadarajan modules. www.numdam.org. 2016-04-23.
4. König. Steffen. Mazorchuk. Volodymyr. 2002-01-01. Enright's completions and injectively copresented modules. Transactions of the American Mathematical Society. 354. 7. 2725–2743. 10.1090/S0002-9947-02-02958-6. 0002-9947. free.
5. Jakelić. Dijana. 2007-06-01. On crystal bases and Enright's completions. Journal of Algebra. 312. 1. 111–131. 10.1016/j.jalgebra.2006.11.045. math/0512506. 120487.
6. Khomenko. Oleksandr. Mazorchuk. Volodymyr. 2004-10-15. On Arkhipov's and Enright's functors. Mathematische Zeitschrift. en. 249. 2. 357–386. 10.1007/s00209-004-0702-8. 121941150. 0025-5874.
7. Deodhar. Vinay V.. 1980-06-01. On a construction of representations and a problem of Enright. Inventiones Mathematicae. en. 57. 2. 101–118. 10.1007/BF01390091. 0020-9910. 1980InMat..57..101D. 121286075.
8. Web site: Past Fellows. www.sloan.org. 2016-03-29.
9. Book: Duflo, Michel. 1979-01-01. Springer Berlin Heidelberg. 9783540092438. Lecture Notes in Mathematics. 22–40. fr. 10.1007/bfb0069971. Séminaire Bourbaki vol. 1977/78 Exposés 507–524. 710. Représentations de carré intégrable des groupes semi-simples réels. http://www.numdam.org/item/SB_1977-1978__20__22_0/.