Geodesic
Tensor operators of the Lie algebras $\mathfrak u(m)$ and $\mathfrak o(\nu)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 3, pp. 474-479 Cet article a éte moissonné depuis la source Math-Net.Ru

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Computationally simple expressions are obtained for the matrix elements of the tensor operators of the Lie algebras $\mathfrak u(m)$ and $\mathfrak o(\nu)$ in bases of irreducible representations. They are obtained in the form of Bell polynomials of sums of powers of the hook lengths $p_{ij}$. Recursion relations and generating functions are also found. An example of the use of the obtained expressions in nuclear physics is given. 
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     title = {Tensor operators of~the {Lie} algebras $\mathfrak u(m)$ and $\mathfrak o(\nu)$},
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S. V. Lyudkovskii. Tensor operators of the Lie algebras $\mathfrak u(m)$ and $\mathfrak o(\nu)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 3, pp. 474-479. http://geodesic.mathdoc.fr/item/TMF_1990_82_3_a13/

[1] Okubo S., J. Math. Phys., 16:3 (1975), 528–535 | DOI | MR | Zbl

[2] Louck J. D., Biedenham L. C., J. Math. Phys., 11:8 (1970), 2368–2414 | DOI | MR | Zbl

[3] Group theoretical methods in physics, Lecture notes in physics, 94, Springer-Verlag, Berlin–Heidelberg–New York, 1979, P. 420. ; 135, 1980, P. 349, 382. | MR | Zbl

[4] March N., Yang U., Sampantkhar S., Problema mnogikh tel v kvantovoi mekhanike, Mir, M., 1969, S. 207, 291. | MR

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

[6] Riordan Dzh., Kombinatornye tozhdestva, Nauka, M., 1982, S. 173–184. | MR | Zbl

[7] Gelfand I. M., Tsetlin M. L., DAN SSSR, 71:5 (1950), 825–828 | MR | Zbl

[8] Gelfand I. M., Tsetlin M. L., DAN SSSR, 71:6 (1950), 1017–1020 | MR | Zbl