Harish-Chandra

:for|the character in Hindu mythology|Harishchandra

Harish-Chandra (11 October 1923-16 October 1983) was an Indian-born American mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups. From 1968, until his death in 1983, he was IBM von Neumann Professor in the School of Mathematics at the Institute for Advanced Study, Princeton. He was a Member of the National Academy of Sciences of the U.S. and a Fellow of the Royal Society. The Harish-Chandra Research Institute, in Allahabad, India, is named in his honour.

Early studies

Harish-Chandra (Harish Chandra Mehrotra) was born in Kanpur (then Cawnpore), British India. His was educated at BNSD Intermediate College, Kanpur, and at the University of Allahabad. After receiving his Masters Degree in 1943, he moved to Bangalore for further studies. In 1945, he moved to University of Cambridge as a research student of Paul Dirac. While at Cambridge, he attended lectures by Wolfgang Pauli, and during one of them pointed out a mistake in Pauli's work. The two were to become life long friends. During this time he became increasingly interested in mathematics. He obtained his PhD in 1947 and during the same year he moved to the USA.

When Dirac visited Princeton, Harish-Chandra worked as his assistant.

Work in mathematics

He was influenced by the mathematicians Hermann Weyl and Claude Chevalley. From 1950 to 1963 was at the Columbia University and carried out some of his best research, especially on representations of semisimple Lie groups. [Harish-Chandra, On some applications of the universal enveloping algebra of a semisimple Lie algebra, Trans. Amer. Math. Soc., 37 (1951), 813–818.] During this period he established as his special area the study of the discrete series representations of semisimple Lie groups — which are the closest analogue of the Peter-Weyl theory in the non-compact case. The methods were formidable and inductive, using Lie group decompositions.

He is also known for work with Armand Borel founding the theory of arithmetic groups; and for papers on finite group analogues. He enunciated a "philosophy of cusp forms", a precursor of the Langlands philosophy".

He was a faculty member at the Institute for Advanced Study in New Jersey from 1963. He was appointed IBM von Neumann Professor in 1968.

Events in the memory of Harish-Chandra

The mathematics department of V.S.S.D college, Kanpur celebrates his birthday every year in different forms, which includes lectures from students and professors from various colleges, institutes and students visit to Harish-Chandra Research Institute. Dr. T. N. Trivedi, head of the mathematics department of V.S.S.D College has been very instrumental in organizing the events.

Harish-Chandra Research Institute

Indian Government honoured him by naming an institute dedicated to Theoretical Physics and Mathematics, after him, in Allahabad, India. The institute is known as "Harish-Chandra Research Institute" or shortly, HRI.

Awards

Harish-Chandra was a Fellow of the Royal Society and Fellow of National Academy of Sciences. He was the recipient of the Cole Prize of the American Mathematical Society, in 1954. The Indian National Science Academy honoured him with the Srinivasa Ramanujan Medal in 1974.

Death

He died of a heart attack in 1983, during a conference in Princeton in honour of Armand Borel's 60th birthday. A similar conference in his honour, scheduled for the following year, was not to take place. He is survived by his wife, Lalitha, and his daughters Premala (Premi), and Devaki.

Books

*V S Varadarajan (ed.), Harish-Chandra, Collected papers I (Springer-Verlag, New York, 1984).
*V S Varadarajan (ed.), Harish-Chandra, Collected papers II (Springer-Verlag, New York, 1984).
*V S Varadarajan (ed.), Harish-Chandra, Collected papers III (Springer-Verlag, New York, 1984).
*V S Varadarajan (ed.), Harish-Chandra, Collected papers IV (Springer-Verlag, New York, 1984).

Articles

*http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Harish-Chandra.html
*A Borel, Some recollections of Harish-Chandra, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer. Math. Soc., Providence, RI, 2000), 37-41.
*A Borel, Some recollections of Harish-Chandra, Current Sci. 65 (12) (1993), 919-921.
*S Helgason, Harish-Chandra memorial talk, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer. Math. Soc., Providence, RI, 2000), 43-45.
*S Helgason, Harish-Chandra and his mathematical legacy : some personal recollections, Current Sci. 74 (10) (1998), 921-924. *R A Herb, Harish-Chandra and his work, Bull. Amer. Math. Soc. 25 (1991), 1-17.
*R A Herb, Harish-Chandra and his work, A joint AMS-MAA lecture presented in San Francisco, California, January 1991. AMS-MAA Joint Lecture Series (Amer. Math. Soc., Providence, RI, 1991), videocassette.
*R A Herb, An elementary introduction to Harish-Chandra's work, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer. Math. Soc., Providence, RI, 2000), 59-75.
*V Kumar Murty, Ramanujan and Harish-Chandra, The Mathematical Intelligencer 15 (2), 33-39.
*R P Langlands, Harish-Chandra, Biographical Memoirs of Fellows of the Royal Society of London 31 (1985), 199-225.
*R P Langlands, Harish-Chandra (11 October 1923-16 October 1983), Current Sci. 65 (12) (1993), 922--936.
*R P Langlands, Harish-Chandra memorial talk, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer. Math. Soc., Providence, RI, 2000), 47-49.
*R P Langlands, Harish-Chandra (1923-1983), in Some eminent Indian mathematicians of the twentieth century (Math. Sci. Trust Soc., New Delhi, 1990), 45-56.
*G D Mostow, Harish-Chandra memorial talk, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer. Math. Soc., Providence, RI, 2000), 51-53.
*N Mukunda, Dirac, Harish-Chandra and the unitary representations of the Lorentz group, Current Sci. 65 (12) (1993), 936-940.
*Remembering Harish-Chandra, in Current trends in mathematics and physics (Narosa, New Delhi, 1995), 208-220.
*S L Srivastava, About Harish Chandra, Ganita-Bharati. Bulletin of the Indian Society for the History of Mathematics 8 (1-4) (1986), 42-43.
*V S Varadarajan, Harish-Chandra (1923- 1983), Math. Intelligencer 6 (3) (1984), 9-13, 19.
*V S Varadarajan, Harish-Chandra 1923- 1983, J. Indian Math. Soc. (N.S.) 56 (1-4) (1991), 190-215.
*V S Varadarajan, Harish-Chandra and his mathematical work, Current Sci. 65 (12) (1993), 918-919.
*V S Varadarajan, Harish-Chandra, his work, and its legacy, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer. Math. Soc., Providence, RI, 2000), 1-35.
*V S Varadarajan, Harish-Chandra memorial talk, in The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998 (Amer. Math. Soc., Providence, RI, 2000), 55-57.
*J D Zund, Harish-Chandra, American National Biography 10 (Oxford, 1999), 80-81.

See also

* Harish-Chandra class
* Harish-Chandra homomorphism
* admissible representation
* infinitesimal character

Notes

References

*cite journal |last=Langlands |first=R. P. |authorlink=Robert Langlands |year=1985 |month=November |title=Harish-Chandra. 11 October 1923-16 October 1983|journal=Biographical Memoirs of Fellows of the Royal Society | publisher=Royal Society | location=London |volume=31 |issue= |pages=199–225 |url=http://www.jstor.org/view/00804606/ap030033/03a00080/0 |doi=10.1098/rsbm.1985.0008 |format=dead link|date=June 2008 – ^{[http://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3ALanglands+intitle%3AHarish-Chandra.+11+October+1923-16+October+1983&as_publication=%5B%5BBiographical+Memoirs+of+Fellows+of+the+Royal+Society%5D%5D&as_ylo=1985&as_yhi=1985&btnG=Search Scholar search]}

External links

*MacTutor Biography|id=Harish-Chandra
* [http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/miscellaneous.html]
* [http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/harish-ps.pdf]
* [http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/harish2-ps.pdf]
* [http://www.mri.ernet.in/hri/harish-chandra#LANGLANDS1985HC brief bography from HRI website]
* [http://query.nytimes.com/gst/fullpage.html?res=9805E7DF123BF93AA25753C1A965948260 Obituary : Harish-Chandra, New York Times (19 October 1983)]
* [http://www.mri.ernet.in Harish-Chandra Research Institute, Allahabad, India]
* [http://www.indiaeducation.ernet.in/insitutions/PROFILENEW.ASP?no=U00036#in HRI]
*References for Harish-Chandra [http://www-groups.dcs.st-andrews.ac.uk/history/References/Harish-Chandra.html]
*Biography in Dictionary of Scientific Biography (New York 1970-1990).