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Harish Chandra Verma (born 3 April 1952), popularly known as HCV, is an Indian experimental physicist, author and emeritus professor of the Indian Institute of Technology Kanpur. In 2021, he was awarded the Padma Shri , the fourth highest civilian award, by the Government of India for his contribution to Physics Education. [ 1 ]
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.
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 ...
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 ...
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.
A particularly important special case is the Harish-Chandra isomorphism identifying the center of the universal enveloping algebra with the invariant polynomials on a Cartan subalgebra. In the case of the K -invariant elements of the universal enveloping algebra for a maximal compact subgroup K , the Harish-Chandra homomorphism was studied by ...