Harish-Chandra
Encyclopedia
Harish-Chandra also called Nagari , is an abugida alphabet of India and Nepal...
: हरिश्चन्द्र, Harish Chandra Mehrotra; 11 October 1923 – 16 October 1983) was an India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, who did fundamental work in representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
, especially Harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
on semisimple Lie groups.
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 Indian Institute of Science,Bangalore for further studies in theoretical physics and worked with H.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 PauliWolfgang Pauli
Wolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...
, 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
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
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...
von Neumann Professor in the School of Mathematics at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
, rinceton, New Jersey,Princeton.
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
Armand Borel
Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993...
'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 WeylHermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
and Claude Chevalley
Claude Chevalley
Claude Chevalley was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups...
. From 1950 to 1963 he was at the Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
and worked on representations of semisimple Lie groups. During this period he established as his special area the study of the discrete series representation
Discrete series representation
In mathematics, a discrete series representation is an irreducible unitary representation of a locally compact topological group G that is a subrepresentation of the left regular representation of G on L²...
s 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
Armand Borel
Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993...
on the theory of arithmetic group
Arithmetic group
In mathematics, an arithmetic group in a linear algebraic group G defined over a number field K is a subgroup Γ of G that is commensurable with G, where O is the ring of integers of K. Here two subgroups A and B of a group are commensurable when their intersection has finite index in each of them...
s; 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 SciencesUnited States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
of the U.S.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
and a Fellow of the Royal Society.
He was the recipient of the Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
, in 1954. The Indian National Science Academy
Indian National Science Academy
The Indian National Science Academy , New Delhi is the apex body of Indian scientists representing all branches of science & technology.-History:...
honoured him with the Srinivasa Ramanujan Medal
Srinivasa Ramanujan Medal
The Srinivasa Ramanujan Medal, named after the Indian mathematician Srinivasa Ramanujan, is awarded by the Indian National Science Academy for work in the mathematical sciences.Past recipients include:*1962 S. Chandrasekhar*1964 B. P. Pal...
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
Harish-Chandra Research Institute
The Harish-Chandra Research Institute is a research institution, named after the mathematician Harish-Chandra, located in Allahabad, Uttar Pradesh, India. It is an autonomous institute, funded by the Department of Atomic Energy of the Government of India...
, an institute dedicated to Theoretical Physics and Mathematics, after him.
See also
- Harish-Chandra's c-functionHarish-Chandra's c-functionIn mathematics, Harish-Chandra's c-function is a function related to the intertwining operator between two principal series representations, that appears in the Plancherel measure for semisimple Lie groups...
- Harish-Chandra's character formula for discrete series representations
- Harish-Chandra homomorphismHarish-Chandra homomorphismIn mathematics, the Harish-Chandra isomorphism, introduced by ,is an isomorphism of commutative rings constructed in the theory of Lie algebras...
- Harish-Chandra isomorphism identifying the center of the universal enveloping algebra with polynomial invariants of the Weyl group.
- Harish-Chandra moduleHarish-Chandra moduleIn mathematics, specifically in the representation theory of Lie groups, a Harish-Chandra module is a representation of a real Lie group, associated to a general representation, with regularity and finiteness conditions...
- Harish-Chandra's regularity theoremHarish-Chandra's regularity theoremIn mathematics, Harish-Chandra's regularity theorem, introduced by , states that every invariant eigendistribution on a semisimple Lie group, and in particular every character of an irreducible unitary representation on a Hilbert space, is given by a locally integrable function...
implying that the character of an irreducible representation is locally integrable - Harish-Chandra's Schwartz spaceHarish-Chandra's Schwartz spaceIn mathematical abstract harmonic analysis, Harish-Chandra's Schwartz space is a space of functions on a semisimple Lie group whose derivatives are rapidly decreasing, studied by...
- Harish-Chandra theoremHarish-Chandra theoremIn matheamtics, Harish-Chandra theorem may refer to one of several theorems due to Harish-Chandra,including:*Harish-Chandra's theorem on the Harish-Chandra isomorphism*Harish-Chandra's classification of discrete series representations...
- Harish-Chandra transformHarish-Chandra transformIn mathematical representation theory, the Harish-Chandra transform is a linear map from functions on a reductive Lie group to functions on a parabolic subgroup...
- Harish-Chandra's Ξ functionHarish-Chandra's Ξ functionIn mathematical harmonic analysis, Harish-Chandra's Ξ function is a special spherical function on a semisimple Lie group, studied by .Harish-Chandra used it to define Harish-Chandra's Schwartz space....