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词条 Bertram Kostant
释义

  1. Early life and education

  2. Career in mathematics

  3. Awards and honors

  4. Selected publications

  5. See also

  6. Notes

  7. References

{{Infobox scientist
| name = Bertram Kostant
| image = Bertram Kostant.jpeg
| image_size = 230px
| caption = Bertram Kostant at a workshop on “Enveloping Algebras and Geometric Representation Theory” in Oberwolfach, 2009
| birth_date = {{Birth date|1928|05|24}}
| birth_place = Brooklyn, New York
| death_date = {{death date and age|2017|02|02|1928|05|24}}
| death_place = Roslindale, Massachusetts
| nationality = American
| fields = Mathematics
| workplaces = Massachusetts Institute of Technology
University of California, Berkeley
| alma_mater = Purdue University
University of Chicago (PhD)
| thesis_title = Representations of a Lie algebra and its enveloping algebra on a Hilbert space
| doctoral_advisor = Irving Segal
| doctoral_students = Arlie Petters
James Lepowsky
Stephen Rallis
James Harris Simons
Moss Sweedler
David Vogan
Birgit Speh
| known_for = Kostant partition function
Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants
| awards = Wigner Medal (2016)
}}Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician.[1]

Early life and education

Kostant grew up in New York City, where he graduated from Stuyvesant High School in 1945.[2] He went on to obtain an undergraduate degree in mathematics from Purdue University in 1950. He earned his Ph.D. from the University of Chicago in 1954, under the direction of Irving Segal, where he wrote a dissertation on representations of Lie groups.

Career in mathematics

After time at the Institute for Advanced Study, Princeton University, and the University of California, Berkeley, he joined the faculty at the Massachusetts Institute of Technology, where he remained until his retirement in 1993. Kostant's work has involved representation theory, Lie groups, Lie algebras, homogeneous spaces, differential geometry and mathematical physics, particularly symplectic geometry. He has given several lectures on the Lie group E8.[3] He has been one of the principal developers of the theory of geometric quantization. His introduction of the theory of prequantization has led to the theory of quantum Toda lattices. The Kostant partition function is named after him. With Gerhard Hochschild and Alex F. T. W. Rosenberg, he is one of the namesakes of the Hochschild–Kostant–Rosenberg theorem which describes the Hochschild homology of some algebras.[4]

His students include James Harris Simons, James Lepowsky, Moss Sweedler, David Vogan, and Birgit Speh. At present he has more than 100 mathematical descendants.

Awards and honors

Kostant's many honors include election to the National Academy of Sciences in 1978. In 2012 he became a fellow of the American Mathematical Society.[5] He was an Invited Speaker of the ICM with talk Orbits and quantization theory in 1970 at Nice.[6]

Selected publications

  • {{cite journal|title=Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold|journal=Trans. Amer. Math. Soc.|volume=80|year=1955|pages=528–542|doi=10.1090/S0002-9947-1955-0084825-8}}
  • {{cite journal|title=A formula for the multiplicity of a weight|journal=Trans. Amer. Math. Soc.|volume=93|year=1959|pages=53–73|doi=10.1090/S0002-9947-1959-0109192-6|pmc=528626}}
  • {{cite journal|title=Lie algebra cohomology and the generalized Borel-Weil theorem|journal=Annals of Mathematics|year=1961|volume=74|issue=2|pages=329–387|doi=10.2307/1970237}}
  • {{cite journal|title=Lie group representations on polynomial rings|journal=American Journal of Mathematics|volume=85|issue=3|year=1963|pages=327–404|doi=10.2307/2373130}}
  • {{cite journal|title=On the existence and irreducibility of certain series of representations|journal=Bulletin of the American Mathematical Society|volume=75|issue=4|year=1969|pages=627–642|doi=10.1090/S0002-9904-1969-12235-4}}
  • {{cite book|year=1970|chapter=Quantization and unitary representations|title=In: Lectures in modern analysis and applications III|series=Lecture Notes in Mathematics 170|pages=87–208|doi=10.1007/BFb0079068}}
  • with Louis Auslander: {{cite journal|title=Polarization and unitary representations of solvable Lie groups|journal=Inventiones mathematicae|year=1971|volume=14|pages=255–354|doi=10.1007/BF01389744}}
  • with Stephen Rallis: {{cite journal|title=Orbits and representations associated with symmetric spaces|journal=American Journal of Mathematics|volume=93|issue=3|year=1971|pages=753–809|doi=10.2307/2373470}}
  • {{cite journal|title=On convexity, the Weyl group and the Iwasawa decomposition|journal=Annales Scientifiques de l'École Normale Supérieure|volume=6|issue=4|pages=413–455|year=1973|url=http://eudml.org/doc/81923}}
  • {{cite book|chapter=Graded manifolds, graded Lie theory, and prequantization|title=In: Differential Geometrical Methods in Mathematical Physics|series=Lecture Notes in Math 570|year=1977|pages=177–306|doi=10.1007/Bfb0087788}}
  • {{cite journal|year=1978|title=On Whittaker vectors and representation theory|journal=Inventiones mathematicae|volume=48|issue=2|pages=101–184|doi=10.1007/BF01390249}}
  • with David Kazhdan and Shlomo Sternberg: {{cite journal|journal=Communications on Pure and Applied Mathematics|volume=31|issue=4|year=1978|pages=481–507|title=Hamiltonian group actions and dynamical systems of Calogero type|doi=10.1002/cpa.3160310405}}
  • {{cite journal|title=The solution to a generalized Toda lattice and representation theory|journal=Advances in Mathematics|volume=34|issue=3|year=1979|pages=195–338|doi=10.1016/0001-8708(79)90057-4}}
  • with Shrawan Kumar: {{cite journal|title=The nil Hecke ring and cohomology of GP for a Kac-Moody group G|journal=Advances in Mathematics|volume=62|issue=3|year=1986|pages=187–237|doi=10.1016/0001-8708(86)90101-5}}
  • with Shlomo Sternberg: {{cite|title=Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras|journal=Annals of Physics|volume=176|issue=1|year=1987|pages=49–113|doi=10.1016/0003-4916(87)90178-3}}
  • {{cite journal|title=On Laguerre polynomials, Bessel functions, Hankel transform and a series in the unitary dual of the simply-connected covering group of |journal=Represent. Theory|volume=4|year=2000|pages=181–224|doi=10.1090/S1088-4165-00-00096-0}}
  • with Gerhard Hochschild and Alex Rosenberg: {{cite book|chapter=Differential forms on regular affine algebras|title=In: Collected Papers|pages=265–290|publisher=Springer|location=New York|year=2009|doi=10.1007/b94535_14}} (Reprinted from Trans. Amer. Math. Soc., vol. 102, no. 3, March 1962, pp. 383–408)
  • {{cite book|chapter=The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group|title=In: Collected Papers|year=2009|pages=130–189|doi=10.1007/b94535_11}} (Reprinted from the Amer. J. Math., vol. 81, no. 4, Oct. 1959)

See also

  • Kostant's convexity theorem
  • Kostant polynomial

Notes

1. ^{{cite web|url=http://news.mit.edu/2017/bertram-kostant-professor-emeritus-mathematics-dies-0216|title=Bertram Kostant, professor emeritus of mathematics, dies at 88|website=MIT News|date=16 February 2017}}
2. ^{{cite web |url=http://www-math.mit.edu/~kostant |title=Professor Kostant's Homepage |publisher=MIT Math Department |accessdate=2007-10-31}}
3. ^{{cite web |url=http://math.ucr.edu/home/baez/kostant/ |title=On Some Mathematics in Garrett Lisi's 'E8 Theory of Everything' |accessdate=2008-06-15 |author=Bertram Kostant |date=2008-02-12 |work= UC Riverside mathematics colloquium }}
4. ^{{citation|url=http://ncatlab.org/nlab/show/Hochschild-Kostant-Rosenberg+theorem|title=Hochschild-Kostant-Rosenberg theorem|work=nLab|date=April 8, 2014|first=Tim|last=Porter}}.
5. ^List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
6. ^Kostant, Bertram. "Orbits and quantization theory." {{Webarchive|url=https://web.archive.org/web/20150326195126/http://www.mathunion.org/ICM/ICM1970.2/Main/icm1970.2.0395.0406.ocr.pdf |date=2015-03-26 }} In Actes, Congrès intern. Math., Nice, vol. 2, pp. 395–400. 1970.

References

  • Kostant's home page at MIT
  • {{MathGenealogy|6442}}
  • {{cite book | author=Brylinski, Jean-Luc (editor) | title=Lie Theory and Geometry, In Honor of Bertram Kostant | publisher=Boston, Birkhäuser | year=1994 | isbn=0-8176-3761-3}}
{{Authority control}}{{DEFAULTSORT:Kostant, Bertram}}

16 : 1928 births|2017 deaths|20th-century American mathematicians|21st-century American mathematicians|Members of the United States National Academy of Sciences|Fellows of the American Mathematical Society|Institute for Advanced Study visiting scholars|Stuyvesant High School alumni|Purdue University alumni|University of Chicago alumni|Princeton University faculty|University of California, Berkeley faculty|Massachusetts Institute of Technology faculty|Guggenheim Fellows|People from Brooklyn|Mathematicians from New York (state)
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