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Harish-Chandra Mehrotra was born in Kanpur. [7] He was educated at B.N.S.D. College, Kanpur and at the University of Allahabad. [8] After receiving his master's degree in physics in 1940, he moved to the Indian Institute of Science, Bangalore for further studies under Homi J. Bhabha.
In mathematics, the Harish-Chandra isomorphism, introduced by Harish-Chandra (), is an isomorphism of commutative rings constructed in the theory of Lie algebras.The isomorphism maps the center (()) of the universal enveloping algebra of a reductive Lie algebra to the elements () of the symmetric algebra of a Cartan subalgebra that are invariant under the Weyl group.
Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. One of such works is Hindu numeral system which is predominantly used today and is likely to be used in the future.
Harish-Chandra, mathematician and physicist (1923–1983 CE) Ranjan Roy Daniel, physicist (1923–2005 CE) M. S. Swaminathan, agronomist (1925–2023 CE) Nitya Anand, medicinal chemist (1925–2024 CE) Raja Ramanna, nuclear physicist (1925–2004 CE) Narinder Singh Kapany, physicist (1926–2020 CE) Syed Zahoor Qasim, marine biologist (1926 ...
In mathematics, specifically in the representation theory of Lie groups, a Harish-Chandra module, named after the Indian mathematician and physicist Harish-Chandra, is a representation of a real Lie group, associated to a general representation, with regularity and finiteness conditions.
Harish-Chandra (1978, 1999) proved a similar theorem for semisimple p-adic groups. Harish-Chandra (1955, 1956) had previously shown that any invariant eigendistribution is analytic on the regular elements of the group, by showing that on these elements it is a solution of an elliptic differential equation. The problem is that it may have ...
The definition of the Schwartz space uses Harish-Chandra's Ξ function and his σ function. The σ function is defined by = ‖ ‖for x=k exp X with k in K and X in p for a Cartan decomposition G = K exp p of the Lie group G, where ||X|| is a K-invariant Euclidean norm on p, usually chosen to be the Killing form.
is called the character (or global character or Harish-Chandra character) of the representation. The character Θ π is a distribution on G that is invariant under conjugation, and is an eigendistribution of the center of the universal enveloping algebra of G , in other words an invariant eigendistribution, with eigenvalue the infinitesimal ...