# Harish-Chandra: Most Underrated Mathematician Ever

From our personal viewpoint, the Indian origin with American citizenship mathematician “Harish-Chandra” should be considered as the most underrated mathematician in history. Harish-Chandra is awarded the Fellowship of Royal Society. Harish-Chandra is born in Kanpur in 1923 and did his graduation from the University of Allahabad (BNSD College). Here is a Harish-Chandra short note and especially focuses on his early life and inventions.

## Harish-Chandra: Most Underrated Mathematician Ever

Some of Harish Chandra’s mathematical innovations and researches:

- Harish-Chandra’s c-function
- Harish-Chandra homomorphism
- Harish-Chandra isomorphism
- Harish-Chandra’s character formula
- Harish-Chandra module
- Harish-Chandra’s regularity theorem
- Harish-Chandra’s Schwartz space

#### Harish-Chandra homomorphism:

A homomorphism from a subalgebra of the universal enveloping algebra of a semisimple Lie algebra to the **universal enveloping algebra** (algebra that contains all representations of a Lie algebra) of a subalgebra. A particularly special case is the Harish-Chandra isomorphism identifying the center of the universal enveloping algebra with the never-changing polynomials on a Cartan subalgebra.

#### Harish-Chandra Module:

A representation of a real Lie group, connected to a general representation, with regularity and limit conditions. When the associated representation is a (g,K)-module, then its Harish-Chandra module is a representation with desirable factorization properties.

**Check**: Ramanujan Magic Square and What’s Unique in its Algorithm

Chandra’s regularity theorem states that: “Every invariant edge distribution 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.”

#### Harish-Chandra Early Life

After receiving his MSc in Physics in 1943, he moved to the IISc – Indian Institute of Science, Bangalore for further studies in theoretical physics and worked with Homi J. Bhabha (one of the ISRO’s founders). Professor Harish-Chandra began his work in the theory of elementary particles, but he turned in 1949 from physics to pure mathematics.

#### Awards & Honors

He was the recipient of the Cole Prize of the American Mathematical Society, in 1954. The INS Academy honored him with the Srinivasa Ramanujan Medal in 1974. In 1981, Harish received an honorary degree from Yale University.

Hence, Professor Harish should be considered the most underrated mathematician ever.