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# Harish-Chandra

Harish-Chandra FRS[1] (Devanāgarī: हरिश्चन्द्र, Harish Chandra Mehrotra; 11 October 1923 – 16 October 1983) was an Indian mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups.[2][3][4]

Life

Harish-Chandra was born in Kanpur (then Cawnpore), British India. He was educated at B.N.S.D. College, Kanpur, and at the University of Allahabad. After receiving his masters degree in Physics in 1943, he moved to the Indian Institute of Science, Bangalore for further studies in theoretical physics and worked with Homi J. Bhabha.

In 1945, he moved to University of Cambridge, Cambridge and worked as a research student under 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. At Cambridge he obtained his PhD in 1947.

When Dirac visited Institute of Advanced Study, Princeton, U.S.A. in 1947/48 he brought Harish-Chandra as his assistant. It was at this stage that Harish-Chandra decided to change over from physics to mathematics.

He was a faculty member at the Institute for Advanced Study, Princeton, New Jersey from 1963.

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, New Jersey.

He died of a heart attack while on an evening walk on October 16, 1983, during a conference in Princeton in honour of Armand Borel's 60th birthday. A similar conference for his 60th birthday, scheduled for the following year, instead became a memorial conference. He is survived by his wife, Lalitha (Lily), and his daughters Premala (Premi), and Devaki.

Work in mathematics

He was influenced by the mathematicians Hermann Weyl and Claude Chevalley. From 1950 to 1963 he was at the Columbia University and worked on representations of semisimple Lie groups. During this period he established as his special area the study of the discrete series representations of semisimple Lie groups, which are analogues of the Peter–Weyl theory in the non-compact case.

He is also known for work with Armand Borel on 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.

Honors and awards

He was a member of the National Academy of Sciences of the U.S. and a Fellow of the Royal Society. [1] 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.

The mathematics department of B.N.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.

The Indian Government named the Harish-Chandra Research Institute, an institute dedicated to Theoretical Physics and Mathematics, after him.

Robert Langlands wrote in a biographical article of Harish-Chandra:

“ He was considered for the Fields Medal in 1958, but a forceful member of the selection committee in whose eyes Thom was a Bourbakist was determined not to have two. So Harish-Chandra, whom he also placed on the Bourbaki camp, was set aside. ”

See also

Harish-Chandra's c-function

Harish-Chandra's character formula for discrete series representations

Harish-Chandra homomorphism

Harish-Chandra isomorphism identifying the center of the universal enveloping algebra with polynomial invariants of the Weyl group.

Harish-Chandra module

Harish-Chandra's regularity theorem implying that the character of an irreducible representation is locally integrable

Harish-Chandra's Schwartz space

Harish-Chandra transform

Harish-Chandra's Ξ function

References

^ a b c Langlands, Robert P. (1985). "Harish-Chandra. 11 October 1923-16 October 1983". Biographical Memoirs of Fellows of the Royal Society 31: 198–193. doi:10.1098/rsbm.1985.0008. JSTOR 769925. edit

^ Harish-Chandra at the Mathematics Genealogy Project

^ O'Connor, John J.; Robertson, Edmund F., "Harish-Chandra", MacTutor History of Mathematics archive, University of St Andrews.

^ Varadarajan, V. S. (1984). "Harish-Chandra (1923–1983)". The Mathematical Intelligencer 6 (3): 9–5. doi:10.1007/BF03024122. edit

Publications

Harish-Chandra (1968), Mars, J. G. M., ed., Automorphic forms on semisimple Lie groups, Lecture Notes in Mathematics, 62, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0098434, ISBN 978-3-540-04232-7, MR0232893

Harish-Chandra (1970), Dijk, G. van, ed., Harmonic analysis on reductive p-adic groups, Lecture Notes in Mathematics, 162, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0061269, ISBN 978-3-540-05189-3, MR0414797

Harish-Chandra (1984), Varadarajan, V. S., ed., Collected papers. Vol. I. 1944–1954., Berlin, New York: Springer-Verlag, ISBN 978-0-387-90782-6, MR726025

Harish-Chandra (1984), Varadarajan, V. S., ed., Collected papers. Vol. II 1955–1958., Berlin, New York: Springer-Verlag, ISBN 978-0-387-90782-6, MR726025

Harish-Chandra (1984), Varadarajan, V. S., ed., Collected papers. Vol. III 1959–1968., Berlin, New York: Springer-Verlag, ISBN 978-0-387-90782-6, MR726025

Harish-Chandra (1984), Varadarajan, V. S., ed., Collected papers. Vol. IV 1970–1983., Berlin, New York: Springer-Verlag, ISBN 978-0-387-90782-6, MR726025

Harish-Chandra (1999), DeBacker, Stephen; Sally, Paul J., eds., Admissible invariant distributions on reductive p-adic groups, University Lecture Series, 16, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-2025-4, MR1702257

Bibliography

Doran, Robert S.; Varadarajan, V. S., eds. (2000), "The mathematical legacy of Harish-Chandra", Proceedings of the AMS Special Session on Representation Theory and Noncommutative Harmonic Analysis, held in memory of Harish-Chandra on the occasion of the 75th anniversary of his birth, in Baltimore, MD, January 9--10, 1998, Proceedings of Symposia in Pure Mathematics, 68, Providence, R.I.: American Mathematical Society, pp. xii+551, ISBN 978-0-8218-1197-9, MR1767886

Srivastava, R. S. L. (1986), "About Harish Chandra", Gaṇita Bhãrati. Indian Society for History of Mathematics. Bulletin 8 (1): 42–43, ISSN 0970-0307, MR888666

Varadarajan, V. S. (2008), "Harish-Chandra", Complete Dictionary of Scientific Biography

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