Harish-Chandra was an Indian-born mathematician and physicist who worked mainly in America and did fundamental work in representation theory, especially on Lie groups.
Mathematical Profile (Excerpt):
- Harish-Chandra worked as a postgraduate research fellow on problems in theoretical physics under Homi Bhabha, at the Indian Institute of Science at Bangalore in Southern India.
- Harish-Chandra began publishing papers on theoretical physics while at Bangalore, and he published a couple of joint papers with Bhabha extending some of Dirac's results.
- Bhabha and Harish-Chandra's teacher, K S Krishnan at Allahabad University, recommended him to Dirac for research work at Cambridge which would lead to Ph.D. degree.
- In 1945 Harish-Chandra went to Gonville and Caius College, Cambridge, where he studied for his doctorate under Dirac's supervision.
- However Harish-Chandra saw comparatively little of his supervisor, giving up attending Dirac's lecture course when he realised that Dirac was essentially reading from one of his books.
- Dirac visited Princeton for the year 1947-48 and Harish-Chandra went to the United States with him, working as his assistant during this time.
- After Dirac returned to Cambridge, Harish-Chandra remained at Princeton for a second year.
- However Harish-Chandra made several attempts to get into algebraic geometry or number theory.
- It was Harish-Chandra who extended the concept of a character of finite-dimensional representations of semisimple Lie groups to the case of infinite-dimensional representations; he proved an analogue of Weyl's character formula.
- Some major contributions by Harish-Chandra's work may be singled out: the explicit determination of the Plancherel measure for semisimple groups, the determination of the discrete series representations, his results on Eisenstein series and in the theory of automorphic forms, his "philosophy of cusp forms", as he called it, as a guiding principle to have a common view of certain phenomena in the representation theory of reductive groups in a rather broad sense, including not only the real Lie groups, but p-adic groups or groups over adele rings.
- Harish-Chandra worked at the Institute of Advanced Study at Princeton from 1963.
- Harish-Chandra received many awards in his career.
- Having been both a physicist and a mathematician it is interesting to see Harish-Chandra's view of their relationship.
- One of his colleagues suggested that Harish-Chandra survives in his work, which faithfully mirrored his personality: intense, lofty, and uncompromising.
Born 11 October 1923, Kanpur, Uttar Pradesh, India. Died 16 October 1983, Princeton, New Jersey, USA.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive