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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.
The Verma module is one particular such highest-weight module, one that is maximal in the sense that every other highest-weight module with highest weight is a quotient of the Verma module. It will turn out that Verma modules are always infinite dimensional; if λ {\displaystyle \lambda } is dominant integral, however, one can construct a ...
If (,) is a representation of G, then the Harish-Chandra module of is the subspace X of V consisting of the K-finite smooth vectors in V. This means that X includes exactly those vectors v such that the map φ v : G V {\displaystyle \varphi _{v}:G\longrightarrow V} via
Harish-Chandra [4] defined the Eisenstein integral by (:::) = () (() ())where: x is an element of a semisimple group G; P = MAN is a cuspidal parabolic subgroup of G; ν is an element of the complexification of a
Harish Chandra or Harish-Chandra may refer to: Harishchandra, a legendary Indian king mentioned in ancient texts; Harish-Chandra Indian American mathematician and physicist (1923–1983) Harish-Chandra Research Institute; Harish-Chandra's c-function; Harish-Chandra's regularity theorem; Harish-Chandra isomorphism; Harish C. Mehta Indian ...
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 ...