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Thomas Jones Enright

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Thomas Jones Enright
Alma materHarvard University
Scientific career
InstitutionsUCSD
Doctoral advisorRamesh A. Gangolli

Thomas Jones Enright is an American mathematician known for his work in the algebraic theory of representations of real reductive Lie groups.

Biography

Thomas J. 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 a year after that in the Institute for Advanced Study at Princeton. N. J. He was chair of the mathematics department of University of California at San Diego from 1986 to 1990.[1]

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 is 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

Bibliography

  • Enright, Thomas J. (1979-01-01). "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. (1975-01-01). "On an Infinitesimal Characterization of the Discrete Series". Annals of Mathematics 102 (1): 1–15. doi:10.2307/1970970.
  • Enright, Thomas J. (1979-01-01). "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. (1980-01-01). "Notes on homological algebra and representations of Lie algebras". Duke Mathematical Journal 47 (1): 1–15. doi:10.1215/S0012-7094-80-04701-8. ISSN 0012-7094.
  • Davidson, Mark G.; Enright, Thomas J.; Stanke, Ronald J. "Differential operators and highest weight representations". Memoirs of the American Mathematical Society 94 (455): 0–0. 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. (1978-03-01). "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. ISSN 0027-8424. PMID 16592507.

References

  1. ^ Support, Math Computing. "UCSD Math | Department History". www.math.ucsd.edu. Retrieved 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. Quatrième Série. 9: 81–101. ISSN 0012-9593.
  3. ^ "Parthasarathy: A generalization of the Enright–Varadarajan modules". www.numdam.org. Retrieved 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. 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". 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". Inventiones mathematicae. 57 (2): 101–118. Bibcode:1980InMat..57..101D. doi:10.1007/BF01390091. ISSN 0020-9910.
  8. ^ "Past Fellows". www.sloan.org. Retrieved 2016-03-29.
  9. ^ Duflo, Michel (1979-01-01). Représentations de carré intégrable des groupes semi-simples réels. Lecture Notes in Mathematics (in French). Springer Berlin Heidelberg. pp. 22–40. doi:10.1007/bfb0069971. ISBN 9783540092438.
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