Newton's formula for

Author:
Tôru Umeda

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3169-3175

MSC (1991):
Primary 17B35, 15A33

DOI:
https://doi.org/10.1090/S0002-9939-98-04557-2

MathSciNet review:
1468206

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Abstract: This paper presents an explicit relation between the two sets which are well-known generators of the center of the universal enveloping algebra of the Lie algebra : one by Capelli (1890) and the other by Gelfand (1950). Our formula is motivated to give an exact analogy for the classical Newton's formula connecting the elementary symmetric functions and the power sum symmetric functions. The formula itself can be deduced from a more general result on Yangians obtained by Nazarov. Our proof is elementary and has an advantage in its direct accessibility.

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Additional Information

**Tôru Umeda**

Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606, Japan

Email:
umeda@kusm.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-98-04557-2

Keywords:
Center of universal enveloping algebra,
Newton's formula,
Hamilton-Cayley theorem

Received by editor(s):
March 28, 1997

Dedicated:
Dedicated to Professor Reiji Takahashi on the occasion of his seventieth birthday

Communicated by:
Roe Goodman

Article copyright:
© Copyright 1998
American Mathematical Society