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A trace formula for semi-simple Lie algebras. (English) Zbl 0437.17001


MSC:

17B20 Simple, semisimple, reductive (super)algebras
22E46 Semisimple Lie groups and their representations

Citations:

Zbl 0308.17007
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References:

[1] H. Casimir , Proc. Koninkl. Akad. Amsterdam , t. 34 , 1931 , p. 844 . Zbl 0002.26503 · Zbl 0002.26503
[2] G. Racah , Rend. Atti. Accad. Naz. Lincei , t. 8 , 1950 , p. 108 . MR 35771 | Zbl 0036.15601 · Zbl 0036.15601
[3] I.M. Gel’fand , Mat. Sbovnik , t. 26 ( 68 ), Nr. 1 , 1950 , p. 103 . MR 33831 | Zbl 0035.30001 · Zbl 0035.30001
[4] C. Chevalley , Amer. J. Math. , t. 77 , 1955 , p. 778 . MR 72877 | Zbl 0065.26103 · Zbl 0065.26103 · doi:10.2307/2372597
[5] A. Klein , J. Math. Plays. , t. 10 , 1963 , p. 1283 .
[6] L.C. Biedenharn , J. Math. Phys. , t. 4 , 1963 , p. 436 . MR 147582 | Zbl 0132.44301 · Zbl 0132.44301 · doi:10.1063/1.1703974
[7] V. Bargmann and M. Moshinsky , Nucl. Phys. , t. 18 , 1960 , p. 697 . MR 121199 | Zbl 0096.23902 · Zbl 0096.23902 · doi:10.1016/0029-5582(60)90438-7
[8] B. Gruber and L. O’Raiffeartaigh , J. Math. Phys. , t. 5 , 1964 , p. 1796 . Zbl 0124.17401 · Zbl 0124.17401 · doi:10.1063/1.1704102
[9] 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
[10] J.D. Louck and L.C. Biedenharn , J. Math. Phys. , t. 11 , 1970 , p. 2368 . MR 297237 | Zbl 0196.14501 · Zbl 0196.14501 · doi:10.1063/1.1665404
[11] M.C.K. Aguilera-Navarro and V.C. Aguilera-Navarro , J. Math. Phys. , t. 17 , 1976 , p. 1173 . Zbl 0332.22020 · Zbl 0332.22020 · doi:10.1063/1.523026
[12] M.K.F. Wong and H.Y. Yeh , J. Math. Phys. , t. 16 , 1975 , p. 1239 . MR 382556 | Zbl 0308.22021 · Zbl 0308.22021 · doi:10.1063/1.522676
[13] C.O. Nwachuka and M.A. Rashid , J. Math. Phys. , t. 17 , 1976 , p. 1611 . Zbl 0336.22011 · Zbl 0336.22011 · doi:10.1063/1.523082
[14] H.S. Green , J. Austral. Math. Soc. , t. 19 (Series B ), 1975 , p. 129 . MR 376844 | Zbl 0359.17002 · Zbl 0359.17002 · doi:10.1017/S0334270000001028
[15] I.N. Bernstein , I.M. Gel’fand and S.I. Gel’fand , J. Funct. Anal. , t. 5 , 1971 , p. 1 . Zbl 0246.17008 · Zbl 0246.17008 · doi:10.1007/BF01075841
[16] B. Kostant , J. Funct. Anal. , t. 20 , 1975 , p. 257 . Zbl 0355.17010 · Zbl 0355.17010 · doi:10.1016/0022-1236(75)90035-X
[17] S. Okubo , J. Math. Phys. , t. 12 , 1977 , p. 2382 .
[18] S.A. Edwards , J. Math. Phys. , t. 1 , 1978 , p. 164 . Zbl 0366.22014 · Zbl 0366.22014 · doi:10.1063/1.523535
[19] J.D. Louck and L.C. Biedenharn , J. Math. Phys. , t. 11 , 1970 , p. 2368 (See Appendix B). MR 297237 | Zbl 0196.14501 · Zbl 0196.14501 · doi:10.1063/1.1665404
[20] A.U. Klimyk , Trans. Amer. Math. Soc. , t. 76 , 1968 . Zbl 0188.29603 · Zbl 0188.29603
[21] J.E. Humphreys , Introduction to Lie Algebras and Representation Theory , Springer-Verlag , New York , Heidelberg , Berlin , 1972 . MR 323842 | Zbl 0254.17004 · Zbl 0254.17004
[22] J. Dixmier , Enveloping Algebras , North-Holland Publ ., Amsterdam , New York , Oxford . MR 498740 | Zbl 0339.17007 · Zbl 0339.17007
[23] R. Steinberg , Bull. Amer. Math. Soc. , t. 67 , 1961 , p. 406 . MR 126508 | Zbl 0115.25605 · Zbl 0115.25605 · doi:10.1090/S0002-9904-1961-10644-7
[24] B. Kostant , Trans. Amer. Math. Soc. , t. 93 , 1959 , p. 53 . MR 109192 | Zbl 0131.27201 · Zbl 0131.27201 · doi:10.2307/1993422
[25] M.D. Gould , On the Matrix Elements of the U(N) Generators , submitted to J. Math. Phys. , and Zbl 0505.22019 · Zbl 0505.22019 · doi:10.1063/1.524749
[26] 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 · Zbl 0445.22010 · doi:10.1063/1.524441
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