Newton's formula for
Author:
Tôru Umeda
Journal:
Proc. Amer. Math. Soc. 126 (1998), 31693175
MSC (1991):
Primary 17B35, 15A33
MathSciNet review:
1468206
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Abstract: This paper presents an explicit relation between the two sets which are wellknown 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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 M. Itoh, Master's thesis at Kyoto University, 1997 Feb..
 [MNO]
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 M. Nazarov, Quantum Berezinian and the classical Capelli identity, Lett. Math. Phys. 21 (1991), 123131. MR 92b:17020
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 H. Ochiai, HarishChandra isomorphism for , private notes (1996).
 [PP1]
 A.M. Perelomov and V.S. Popov, Casimir operators for and , Soviet J. Nuclear Phys. 3 (1966), 676680. MR 34:5446
 [PP2]
 , Casimir operators for the orthogonal and symplectic groups, Soviet J. Nuclear Phys. 3 (1966), 819824. MR 34:5447
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Additional Information
Tôru Umeda
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606, Japan
Email:
umeda@kusm.kyotou.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993998045572
PII:
S 00029939(98)045572
Keywords:
Center of universal enveloping algebra,
Newton's formula,
HamiltonCayley 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
