A trace formula for semi-simple Lie algebras
Gould, M. D.
Annales de l'I.H.P. Physique théorique, Tome 33 (1980), p. 203-219 / Harvested from Numdam
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Publié le : 1980-01-01
@article{AIHPA_1980__32_3_203_0,
     author = {Gould, M. D.},
     title = {A trace formula for semi-simple Lie algebras},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {33},
     year = {1980},
     pages = {203-219},
     mrnumber = {579960},
     zbl = {0437.17001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1980__32_3_203_0}
}

Gould, M. D. A trace formula for semi-simple Lie algebras. Annales de l'I.H.P. Physique théorique, Tome 33 (1980) pp. 203-219. http://gdmltest.u-ga.fr/item/AIHPA_1980__32_3_203_0/

[1] H. Casimir, Proc. Koninkl. Akad. Amsterdam, t. 34, 1931, p. 844. | Zbl 0002.26503

[2] G. Racah, Rend. Atti. Accad. Naz. Lincei, t. 8, 1950, p. 108. | MR 35771 | Zbl 0036.15601

[3] I.M. Gel'Fand, Mat. Sbovnik, t. 26 (68), Nr. 1, 1950, p. 103. | MR 33831 | Zbl 0035.30001

[4] C. Chevalley, Amer. J. Math., t. 77, 1955, p. 778. | MR 72877 | Zbl 0065.26103

[5] A. Klein, J. Math. Plays., t. 10, 1963, p. 1283.

L.C. Biedenharn, J. Math. Phys., t. 4, 1963, p. 436. | MR 147582 | Zbl 0132.44301

V. Bargmann and M. Moshinsky, Nucl. Phys., t. 18, 1960, p. 697. | MR 121199 | Zbl 0096.23902

B. Gruber and L. O'Raiffeartaigh, J. Math. Phys., t. 5, 1964, p. 1796. | Zbl 0124.17401

[6] V.S. Popov and A.M. Perelomov, Sov. J. Nucl. Phys., t. 5, 1967, p. 489

and V.S. Popov and A.M. Perelomov, Sov. J. Nucl. Phys., t. 3, 1966, p. 676. | MR 205620

J.D. Louck and L.C. Biedenharn, J. Math. Phys., t. 11, 1970, p. 2368. | MR 297237 | Zbl 0196.14501

M.C.K. Aguilera-Navarro and V.C. Aguilera-Navarro, J. Math. Phys., t. 17, 1976, p. 1173. | Zbl 0332.22020

M.K.F. Wong and H.Y. Yeh, J. Math. Phys., t. 16, 1975, p. 1239. | MR 382556 | Zbl 0308.22021

C.O. Nwachuka and M.A. Rashid, J. Math. Phys., t. 17, 1976, p. 1611. | Zbl 0336.22011

H.S. Green, J. Austral. Math. Soc., t. 19 (Series B), 1975, p. 129. | MR 376844 | Zbl 0359.17002

[7] I.N. Bernstein, I.M. Gel'Fand and S.I. Gel'Fand, J. Funct. Anal., t. 5, 1971, p. 1. | Zbl 0246.17008

[8] B. Kostant, J. Funct. Anal., t. 20, 1975, p. 257. | Zbl 0355.17010

[9] S. Okubo, J. Math. Phys., t. 12, 1977, p. 2382.

[10] S.A. Edwards, J. Math. Phys., t. 1, 1978, p. 164. | Zbl 0366.22014

[11] J.D. Louck and L.C. Biedenharn, J. Math. Phys., t. 11, 1970, p. 2368 (See Appendix B). | MR 297237 | Zbl 0196.14501

[12] A.U. Klimyk, Trans. Amer. Math. Soc., t. 76, 1968. | Zbl 0188.29603

[13] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1972. | MR 323842 | Zbl 0254.17004

[14] J. Dixmier, Enveloping Algebras, North-Holland Publ., Amsterdam, New York, Oxford. | MR 498740 | Zbl 0339.17007

[15] R. Steinberg, Bull. Amer. Math. Soc., t. 67, 1961, p. 406. | MR 126508 | Zbl 0115.25605

[16] B. Kostant, Trans. Amer. Math. Soc., t. 93, 1959, p. 53. | MR 109192 | Zbl 0131.27201

[17] M.D. Gould, On the Matrix Elements of the U(N) Generators, submitted to J. Math. Phys., and | Zbl 0505.22019

M.D. Gould, An Infinitesimal Approach to Semi-Simple Lie Groups and Raising and Lowering Operators of O(N) and U(N), to appear in J. Math. Phys. | MR 562988 | Zbl 0445.22010