Biography:Thomas Jones Enright

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Short description: American mathematician (1947–2019)
Thomas Jones Enright
Tom at home in San Diego.jpg
BornAugust 15, 1947
Concord, New Hampshire, United States
DiedJanuary 27, 2019(2019-01-27) (aged 71)
San Diego, California, United States
Alma materHarvard University B.S. & University of Washington Ph.D.
AwardsAlfred P. Sloan Research Fellowship
Scientific career
FieldsMathematics
InstitutionsUCSD
Doctoral advisorRamesh A. Gangolli

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 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. doi:10.2307/1971244. 
  • Enright, Thomas J.; Varadarajan, V. S. (1975). "On an Infinitesimal Characterization of the Discrete Series". Annals of Mathematics 102 (1): 1–15. doi:10.2307/1970970. 
  • 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. doi:10.2307/1971244. 
  • 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. ISBN:9780817631352.
  • Enright, T. J.; Wallach, N. R. (1980). "Notes on homological algebra and representations of Lie algebras". Duke Mathematical Journal 47 (1): 1–15. doi: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. doi: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. ISBN:9781493915897.
  • 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. doi:10.1073/pnas.75.3.1063. PMID 16592507. Bibcode: 1978PNAS...75.1063E. 

References

  1. ↑ Support, Math Computing. "UCSD Math | Department History". http://www.math.ucsd.edu/about/department-history/. 
  2. ↑ Wallach, Nolan R. (1976-01-01). "On the Enright–Varadarajan modules: A construction of the discrete series" (in en). Annales Scientifiques de l'École Normale Supérieure. Série 4 9: 81–101. doi:10.24033/asens.1304. ISSN 0012-9593. https://www.zbmath.org/?q=an:0379.22008. 
  3. ↑ "Parthasarathy: A generalization of the Enright–Varadarajan modules". http://www.numdam.org/numdam-bin/fitem?id=CM_1978__36_1_53_0. 
  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. doi:10.1090/S0002-9947-02-02958-6. ISSN 0002-9947. 
  5. ↑ Jakelić, Dijana (2007-06-01). "On crystal bases and Enright's completions". Journal of Algebra 312 (1): 111–131. doi:10.1016/j.jalgebra.2006.11.045. 
  6. ↑ Khomenko, Oleksandr; Mazorchuk, Volodymyr (2004-10-15). "On Arkhipov's and Enright's functors" (in en). Mathematische Zeitschrift 249 (2): 357–386. doi:10.1007/s00209-004-0702-8. ISSN 0025-5874. 
  7. ↑ Deodhar, Vinay V. (1980-06-01). "On a construction of representations and a problem of Enright" (in en). Inventiones Mathematicae 57 (2): 101–118. doi:10.1007/BF01390091. ISSN 0020-9910. Bibcode: 1980InMat..57..101D. 
  8. ↑ "Past Fellows". http://www.sloan.org/sloan-research-fellowships/past-fellows/?L=0%252525252525253FcHash%252525252525253D8310691d61f6bf828bef8d1badc50c0a&tx_sloangrants_sloanfellows%5Baction%5D=list&tx_sloangrants_sloanfellows%5Bcontroller%5D=Fellows&cHash=8f53adde7b4458aff6de5c2679773fee. 
  9. ↑ Duflo, Michel (1979-01-01). "Représentations de carré intégrable des groupes semi-simples réels" (in fr). Séminaire Bourbaki vol. 1977/78 Exposés 507–524. Lecture Notes in Mathematics. 710. Springer Berlin Heidelberg. pp. 22–40. doi:10.1007/bfb0069971. ISBN 9783540092438. http://www.numdam.org/item/SB_1977-1978__20__22_0/. 

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