Abstract:
Compact invertible relationships are obtained between the eigenvalues of the invariant operators for irreducible representations of the classical Lie groups and elementary symmetric polynomials. This continues earlier work of the author [1]. The polynomials of Chebyshev and Bell, and also numbers analogous to Euler numbers are used. Polynomial identities that
express the invariants in terms of sets of independent invariants are given. The use of the obtained expressions in nuclear physics is discussed.
Citation:
S. V. Lyudkovskii, “Compact relationships between invariants of classical lie groups and elementary symmetric polynomials”, TMF, 89:3 (1991), 380–387; Theoret. and Math. Phys., 89:3 (1991), 1281–1286
\Bibitem{Lud91}
\by S.~V.~Lyudkovskii
\paper Compact relationships between invariants of classical lie groups and elementary symmetric polynomials
\jour TMF
\yr 1991
\vol 89
\issue 3
\pages 380--387
\mathnet{http://mi.mathnet.ru/tmf5902}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1146422}
\zmath{https://zbmath.org/?q=an:0762.22021}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 89
\issue 3
\pages 1281--1286
\crossref{https://doi.org/10.1007/BF01017822}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991JA04100004}
Linking options:
https://www.mathnet.ru/eng/tmf5902
https://www.mathnet.ru/eng/tmf/v89/i3/p380
This publication is cited in the following 5 articles:
Dorin Andrica, Sorin Rădulescu, Marius Rădulescu, Springer Optimization and Its Applications, 151, Differential and Integral Inequalities, 2019, 135
Zhi‐Hua Zhang, Hari M. Srivastava, “Some characteristic properties of the weighted particular Schur polynomial mean”, Math Methods in App Sciences, 42:18 (2019), 6459
Moawwad El-Mikkawy, Faiz Atlan, “Remarks on two symmetric polynomials and some matrices”, Applied Mathematics and Computation, 219:16 (2013), 8770
Moawwad El-Mikkawy, Tomohiro Sogabe, “Notes on particular symmetric polynomials with applications”, Applied Mathematics and Computation, 215:9 (2010), 3311
S. V. Lyudkovskii, “Topological Transformation Groups of Manifolds over Non-Archimedean Fields, Their Representations, and Quasi-Invariant Measures, II”, Journal of Mathematical Sciences, 150:4 (2008), 2123–2223
Citation in format AMSBIB
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