A trace formula for semi-simple Lie algebras

M. D. Gould

Annales de l'I.H.P. Physique théorique (1980)

  • Volume: 32, Issue: 3, page 203-219
  • ISSN: 0246-0211

How to cite

top

Gould, M. D.. "A trace formula for semi-simple Lie algebras." Annales de l'I.H.P. Physique théorique 32.3 (1980): 203-219. <http://eudml.org/doc/76071>.

@article{Gould1980,
author = {Gould, M. D.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {trace formula; semi-simple Lie algebras; Harish-Chandra homomorphism; invariants},
language = {eng},
number = {3},
pages = {203-219},
publisher = {Gauthier-Villars},
title = {A trace formula for semi-simple Lie algebras},
url = {http://eudml.org/doc/76071},
volume = {32},
year = {1980},
}

TY - JOUR
AU - Gould, M. D.
TI - A trace formula for semi-simple Lie algebras
JO - Annales de l'I.H.P. Physique théorique
PY - 1980
PB - Gauthier-Villars
VL - 32
IS - 3
SP - 203
EP - 219
LA - eng
KW - trace formula; semi-simple Lie algebras; Harish-Chandra homomorphism; invariants
UR - http://eudml.org/doc/76071
ER -

References

top
  1. [1] H. Casimir, Proc. Koninkl. Akad. Amsterdam, t. 34, 1931, p. 844. Zbl0002.26503
  2. [2] G. Racah, Rend. Atti. Accad. Naz. Lincei, t. 8, 1950, p. 108. Zbl0036.15601MR35771
  3. [3] I.M. Gel'fand, Mat. Sbovnik, t. 26 (68), Nr. 1, 1950, p. 103. Zbl0035.30001MR33831
  4. [4] C. Chevalley, Amer. J. Math., t. 77, 1955, p. 778. Zbl0065.26103MR72877
  5. [5] A. Klein, J. Math. Plays., t. 10, 1963, p. 1283. 
  6. L.C. Biedenharn, J. Math. Phys., t. 4, 1963, p. 436. Zbl0132.44301MR147582
  7. V. Bargmann and M. Moshinsky, Nucl. Phys., t. 18, 1960, p. 697. Zbl0096.23902MR121199
  8. B. Gruber and L. O'Raiffeartaigh, J. Math. Phys., t. 5, 1964, p. 1796. Zbl0124.17401
  9. [6] V.S. Popov and A.M. Perelomov, Sov. J. Nucl. Phys., t. 5, 1967, p. 489 
  10. and V.S. Popov and A.M. Perelomov, Sov. J. Nucl. Phys., t. 3, 1966, p. 676. MR205620
  11. J.D. Louck and L.C. Biedenharn, J. Math. Phys., t. 11, 1970, p. 2368. Zbl0196.14501MR297237
  12. M.C.K. Aguilera-Navarro and V.C. Aguilera-Navarro, J. Math. Phys., t. 17, 1976, p. 1173. Zbl0332.22020
  13. M.K.F. Wong and H.Y. Yeh, J. Math. Phys., t. 16, 1975, p. 1239. Zbl0308.22021MR382556
  14. C.O. Nwachuka and M.A. Rashid, J. Math. Phys., t. 17, 1976, p. 1611. Zbl0336.22011
  15. H.S. Green, J. Austral. Math. Soc., t. 19 (Series B), 1975, p. 129. Zbl0359.17002MR376844
  16. [7] I.N. Bernstein, I.M. Gel'fand and S.I. Gel'fand, J. Funct. Anal., t. 5, 1971, p. 1. Zbl0246.17008
  17. [8] B. Kostant, J. Funct. Anal., t. 20, 1975, p. 257. Zbl0355.17010
  18. [9] S. Okubo, J. Math. Phys., t. 12, 1977, p. 2382. 
  19. [10] S.A. Edwards, J. Math. Phys., t. 1, 1978, p. 164. Zbl0366.22014
  20. [11] J.D. Louck and L.C. Biedenharn, J. Math. Phys., t. 11, 1970, p. 2368 (See Appendix B). Zbl0196.14501MR297237
  21. [12] A.U. Klimyk, Trans. Amer. Math. Soc., t. 76, 1968. Zbl0188.29603
  22. [13] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, Heidelberg, Berlin, 1972. Zbl0254.17004MR323842
  23. [14] J. Dixmier, Enveloping Algebras, North-Holland Publ., Amsterdam, New York, Oxford. Zbl0339.17007MR498740
  24. [15] R. Steinberg, Bull. Amer. Math. Soc., t. 67, 1961, p. 406. Zbl0115.25605MR126508
  25. [16] B. Kostant, Trans. Amer. Math. Soc., t. 93, 1959, p. 53. Zbl0131.27201MR109192
  26. [17] M.D. Gould, On the Matrix Elements of the U(N) Generators, submitted to J. Math. Phys., and Zbl0505.22019
  27. 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. Zbl0445.22010MR562988

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.