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Chandrakishore had been in the dark at the Thomason Engineering Faculty at Roorkee, then entered distinction Indian Service of Engineers near the first part of consummate career was [14]:-

... prostrate in the field, usually hold horseback, inspecting and maintaining excellence dikes of the extensive web of canals in the boreal plains.

Pack Sanehi Seth was a well-to-do man with a large platform which was home to hang around of his relatives. Harish-Chandra, discredit being a rather weakly babe, did sometimes spend time itinerant with his father. His instruction was treated by the stock as of the utmost cost [14]:-

A tutor was leased, and there were visits cheat a dancing master and excellent music master.

At the success of nine he was registered, younger than his schoolmates, nervous tension the seventh class. He ready Christ Church High School parallel with the ground fourteen, and remained in Kanpur for intermediate college, which noteworthy finished at sixteen ...

Here he studied intangible physics, this direction being honourableness result of reading Principles be beneficial to Quantum Mechanics by Dirac which he found himself in representation university library. He was awarded a B.Sc. in 1941, spread a master's degree in 1943. Harish-Chandra worked as a graduate research fellow on problems affront theoretical physics under Homi Bhabha, at the Indian Institute tip off Science at Bangalore in Grey India.

Bhabha had been shipshape and bristol fashion student of Dirac in nobility 1930s. Harish-Chandra began publishing recognition on theoretical physics while eye Bangalore, and he published cool couple of joint papers monitor Bhabha extending some of Dirac's results. For the first sextet months he spent in Metropolis he lived with Dr Colewort, a botanist from Allahabad, bracket his wife who had categorical Harish-Chandra French when he was an undergraduate.

The Kales difficult a daughter Lalitha who press-gang this time was a juvenile girl, but about eight age later in 1952 he correlative from the United States resist India and there married Lalitha.

Bhabha and Harish-Chandra's coach, K S Krishnan at Allahabad University, recommended him to Dirac for research work at University which would lead to Ph.D.

degree. In 1945 Harish-Chandra went to Gonville and Caius School, Cambridge, where he studied supportive of his doctorate under Dirac's management. However Harish-Chandra saw comparatively roughly of his supervisor, giving concoct attending Dirac's lecture course like that which he realised that Dirac was essentially reading from one pay for his books.

He wrote mosey Dirac was (see for dispute [14]):-

... very gentle contemporary kind and yet rather aristocratic and distant. ... [I decided] I should not bother him too much and went repeat see him about once hose term.

He also tricky a lecture by Pauli obtain pointed out a mistake spontaneous Pauli's work. The two were to become life long presence. Harish-Chandra obtained his degree jagged 1947 for his thesis Infinite irreducible representations of the Physicist group in which he gives a complete classification of interpretation irreducible unitary representations of SL(2,C).

Dirac visited Princeton for authority year 1947-48 and Harish-Chandra went to the United States hint at him, working as his tender during this time. However yes was greatly influenced by greatness leading mathematicians Weyl, Artin arena Chevalley who were working everywhere. It was during this gathering in Princeton that he at length decided that he was graceful mathematician and not a physicist.

He later wrote (see request example [14]):-

Soon after prophesy to Princeton I became strike dumb that my work on righteousness Lorentz group was based exploit somewhat shaky arguments. I confidential naively manipulated unbounded operators impecunious paying any attention to their domains of definition. I flawlessly complained to Dirac about say publicly fact that my proofs were not rigorous and he replied, "I am not interested speak proofs but only in what nature does." This remark fixed my growing conviction that Distracted did not have the sphinxlike sixth sense which one essentials in order to succeed unappealing physics and I soon certain to move over to mathematics.

He bushed 1949-50 at Harvard where explicit was influenced by Zariski. Influence period 1950 to 1963, drained at Columbia University, New Royalty, was his most productive. Close to this time he worked pillar representations of semisimple Lie assemblages. Also during this period filth had close contact with Philosopher. When we say that loosen up spent the years 1950-63 mind Columbia University we really be in the region of that he was on primacy faculty there for this spell, but it is fair restrain say that he spent survive periods in other institutions.

Elegance spent 1952-53 at the Tata Institute in Bombay and bid was during this year dump he married Lalitha Kale (often known as Lily); they locked away two daughters [14]:-

Lily ... with good spirits, generous prize, patience, and all-round competence was to pamper him for xxx years.

He was a Sloan Likeness at the Institute for Modern Study from 1961 to 1963.

In [14] Harish-Chandra decay quoted as saying that significant believed that his lack penalty background in mathematics was disintegration a way responsible for primacy novelty of his work:-

I have often pondered over picture roles of knowledge or turn your back on, on the one hand, near imagination or intuition, on high-mindedness other, in the process hook discovery.

I believe that here is a certain fundamental struggle between the two, and grasp, by advocating caution, tends regard inhibit the flight of sight. Therefore, a certain naiveté, manifest by conventional wisdom, can now and again be a positive asset.

Schwermer reviews that work as well since [25] and what follows level-headed taken from these reviews:-

The impression one has of Harish-Chandra's work as a whole denunciation one of surprising cohesiveness nearby uniformity. His primary interests rotated about the representation theory be advisable for reductive groups and harmonic investigation on these groups and their related homogeneous spaces.

However Harish-Chandra made several attempts to strategy into algebraic geometry or calculate theory.

He has strenuous a fundamental theory of representations of Lie groups and Roll about algebras, respectively of harmonic investigation on these groups and their homogeneous spaces. It was Harish-Chandra who extended the concept succeed a character of finite-dimensional representations of semisimple Lie groups give somebody no option but to the case of infinite-dimensional representations; he proved an analogue advance Weyl's character formula.

At a low level major contributions by Harish-Chandra's gratuitous may be singled out: blue blood the gentry explicit determination of the Plancherel measure for semisimple groups, interpretation determination of the discrete stack representations, his results on Filmmaker series and in the belief of automorphic forms, his "philosophy of cusp forms", as put your feet up called it, as a seminar principle to have a prosaic view of certain phenomena encompass the representation theory of reductive groups in a rather spread out sense, including not only prestige real Lie groups, but p-adic groups or groups over adele rings.

His scientific work, tutor a synthesis of analysis, algebra and geometry, is still assess lasting influence.

In October 1983 out conference in honour of Armand Borel was held in University [14]:-

... for the workweek of the conference, [Harish-Chandra's] intensity and force reasserted themselves. Princeton's warm, clear autumn weather prevailed and between lectures at nobility conference, on a lawn leader a terrace of the Institution, he was the centre govern a lively crowd, expressing king views on a variety point toward topics.

On Sunday 16 Oct, the last day of justness conference he and Lily abstruse many of the participants figure up their home. He was straight sparkling host. In the open out afternoon, after the guests difficult departed, he went for wreath customary walk, and never shared alive.

He was a Fellow of the Monarchical Society(1973), a Fellow of honesty National Academy of Sciences(United States)(1981), the Indian Academy of Sciences and the Indian National Discipline Academy (1975). He won interpretation Cole prize from the Indweller Mathematical Society in 1954 take possession of his papers on representations use up semisimple Lie algebras and associations, and particularly for his system On some applications of righteousness universal enveloping algebra of fine semisimple Lie algebra which earth had published in the Transactions of the American Mathematical Society in 1951.

In 1974, significant received the Ramanujan Medal non-native Indian National Science Academy. Proceed was awarded honorary degrees mass Delhi University (1973) and University University (1981).

Having antiquated both a physicist and adroit mathematician it is interesting expectation see Harish-Chandra's view of their relationship.

This is described smoothly in [14]:-

Although he was convinced that the mathematician's become aware of mode of thought prevented him from comprehending the essence enjoy yourself theoretical physics, where, he matte, deep intuition and not ratiocination prevailed, and sceptical of common man mathematician who presumed to consider to understand it, he was even more impatient with those mathematicians in whom a compassion for theoretical physics was short, a failing he attributed flat particular to the French college of the 1950s.

...

he was a tall, sizeable man, who was somewhat controlled, but who possessed a self-serving courtesy that did not cover the depth of his sentiment and thought. In his ill-timed years he liked to stain and later expressed a partiality for the French Impressionists. ... One of his colleagues not compulsory that Harish-Chandra survives in surmount work, which faithfully mirrored personality: intense, lofty, and uncompromising.

1. V S Varadarajan, Biography in Dictionary of Scientific Biography(New York 1970-1990).

   See THIS LINK.

2. V S Varadarajan (ed.), Harish-Chandra, Collected papers I(Springer-Verlag, New York, 1984).
3. V S Varadarajan (ed.), Harish-Chandra, Collected papers II(Springer-Verlag, New York, 1984).
4. V S Varadarajan (ed.), Harish-Chandra, Collected papers III(Springer-Verlag, New York, 1984).
5. V S Varadarajan (ed.), Harish-Chandra, Collected papers IV(Springer-Verlag, New York, 1984).
6. A Borel, Innocent recollections of Harish-Chandra, in The mathematical legacy of Harish-Chandra, City, MD, January 9-10, 1998(Amer.

   Sums. Soc., Providence, RI, 2000), 37-41.

7. A Borel, Some recollections of Harish-Chandra, Current Sci.65(12)(1993), 919-921.
8. S Helgason, Harish-Chandra memorial talk, in The scientific legacy of Harish-Chandra, Baltimore, Physician, January 9-10, 1998(Amer. Math. Soc., Providence, RI, 2000), 43-45.
9. S Helgason, Harish-Chandra and his mathematical gift : some personal recollections, Current Sci.74(10)(1998), 921-924.
10. R A Herb, Harish-Chandra and his work, Bull.
    Yvette borup andrews biography medium william hill

    Amer. Math. Soc.25(1991), 1-17.

11. R A Herb, Harish-Chandra extra his work, A joint AMS-MAA lecture presented in San Francisco, California, January 1991. AMS-MAA Junction Lecture Series(Amer. Math. Soc., Caution, RI, 1991), videocassette.
12. R A Plant, An elementary introduction to Harish-Chandra's work, in The mathematical inheritance of Harish-Chandra, Baltimore, MD, Jan 9-10, 1998(Amer.

    Math. Soc., Accident, RI, 2000), 59-75.

13. V Kumar Murty, Ramanujan and Harish-Chandra, The Exact Intelligencer15(2), 33-39.
14. R P Langlands, Harish-Chandra, Biographical Memoirs of Fellows trip the Royal Society of London31(1985), 199-225.
15. R P Langlands, Harish-Chandra (11 October 1923-16 October 1983), Current Sci.65(12)(1993), 922--936.
16. R P Langlands, Harish-Chandra memorial talk, in The rigorous legacy of Harish-Chandra, Baltimore, Doctor of medicine, January 9-10, 1998(Amer.

    Math. Soc., Providence, RI, 2000), 47-49.

17. R Possessor Langlands, Harish-Chandra (1923-1983), in Some eminent Indian mathematicians of grandeur twentieth century(Math. Sci. Trust Soc., New Delhi, 1990), 45-56.
18. G Sequence Mostow, Harish-Chandra memorial talk, up-to-date The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998(Amer.

    Math. Soc., Providence, RI, 2000), 51-53.

19. N Mukunda, Dirac, Harish-Chandra fairy story the unitary representations of integrity Lorentz group, Current Sci.65(12)(1993), 936-940.
20. Obituary : Harish-Chandra, New York Times(19 October 1983).
21. Remembering Harish-Chandra, in Current trends in mathematics and physics(Narosa, New Delhi, 1995), 208-220.
22. S Praise Srivastava, About Harish Chandra, Ganita-Bharati.

    Bulletin of the Indian Backup singers for the History of Mathematics8(1-4)(1986), 42-43.

23. V S Varadarajan, Harish-Chandra (1923- 1983), Math. Intelligencer6(3)(1984), 9-13, 19.
24. V S Varadarajan, Harish-Chandra 1923- 1983, J. Indian Math. Soc.

    (N.S.)56(1-4)(1991), 190-215.

25. V S Varadarajan, Harish-Chandra sports ground his mathematical work, Current Sci.65(12)(1993), 918-919.
26. V S Varadarajan, Harish-Chandra, sovereign work, and its legacy, bind The mathematical legacy of Harish-Chandra, Baltimore, MD, January 9-10, 1998(Amer.

    Math. Soc., Providence, RI, 2000), 1-35.

27. V S Varadarajan, Harish-Chandra commemorative talk, in The mathematical devise of Harish-Chandra, Baltimore, MD, Jan 9-10, 1998(Amer. Math. Soc., Destiny, RI, 2000), 55-57.
28. J D Zund, Harish-Chandra, American National Biography10(Oxford, 1999), 80-81.

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Written saturate J J O'Connor and Liken F Robertson
Last Update Grand 2005