Geodesic
Compact relationships between invariants of classical lie groups and elementary symmetric polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 3, pp. 380-387 
S. V. Lyudkovskii. Compact relationships between invariants of classical lie groups and elementary symmetric polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 3, pp. 380-387. http://geodesic.mathdoc.fr/item/TMF_1991_89_3_a3/
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     author = {S. V. Lyudkovskii},
     title = {Compact relationships between invariants of classical lie groups and elementary symmetric polynomials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {380--387},
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     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_3_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Lyudkovskii S. V., TMF, 75:2 (1988), 316–320 | MR

[2] Gelfand I. M., Matem. sb., 26 (1950), 103–112 | MR | Zbl

[3] Popov V. S., Perelomov A. M., YaF, 7:2 (1968), 460–469

[4] Perelomov A. M., Popov V. S., Izv. AN SSSR. Ser. matem., 32:6 (1968), 1368–1390 | MR | Zbl

[5] Edwards S. A., J. Math. Phys., 19:1 (1978), 164–167 | DOI | MR | Zbl

[6] Riordan Dzh., Kombinatornye tozhdestva, Nauka, M., 1982 | MR | Zbl