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Quantum-mechanical calculation of the orders of finite simple groups of lie type

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Literature Cited

  1. D. Gorenstein, Finite Simple Groups, Plenum Press, New York (1982).

    Google Scholar 

  2. F. J. Dyson, “Statistical theory of the energy levels of complex systems,” J. Math. Phys.,3, 140 (1962).

    Google Scholar 

  3. A. Rocha-Caridi, Vertex Operators in Mathematics and Physics (eds. J. Lepovsky, S. Mandelstam, and I. Singer), Springer Verlag, New York (1983).

    Google Scholar 

  4. D. J. Gross, J. A. Harvey, E. Martinec, and R. Rohm, Nucl. Phys. B,256, 253 (1985).

    Google Scholar 

  5. D. Gepner and E. Witten, Nucl. Phys. B,278, 493 (1986).

    Google Scholar 

  6. M. Kac, Infinite-Dimensional Lie Algebras, Cambridge University Press (1985).

  7. R. Steinberg, Lectures on Chevalley Groups [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  8. Sh. Hamidi and C. Vafa, Nucl. Phys. B,279, 465 (1987).

    Google Scholar 

  9. H. S. M. Coxeter, Ann. Math.,35, 588 (1934).

    Google Scholar 

  10. T. Springer, The Theory of Invariants [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  11. J. P. Serre, Course of Arithmetic [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  12. G. Anderson and G. Moore, “Rationality in conformal field theory,” Preprint IAS-SNS-HEP-87/69, Princeton University (1987).

  13. M. A. Olshanetsky and A. M. Perelomov, Phys. Rep.,94, 313 (1983).

    Google Scholar 

  14. G. C. Shephard and J. A. Todd, Can. J. Math.,6, 274 (1954); A. M. Cohen, Ann. Scient. Ec. Norm. Sup.,4, 379 (1976).

    Google Scholar 

  15. Yu. I. Manin, Reflections on Arithmetical Physics, Talk at the Poiana-Brasov School on Strings and Conformal Field Theory (1987); P. G. O. Freund and E. Witten, Phys. Lett. B,199, 191 (1987); E. Witten, Commun. Math. Phys.,113, 529 (1987).

  16. M. Kneser, “Semisimple algebraic groups,” in: Algebraic Number Theory [Russian translations], Mir, Moscow (1969); I. M. Gel'fand M. I. Graev, and I. I. Pyatetskii-Shapiro, the Theory of Representations and Automorphic Functions [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  17. E. Witten, “Topological sigma model,” Preprint IAS-PUB-SNS-HEP 88/7, Princeton University (1988).

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Institute of Theoretical and Experimental Physics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 82, No. 3, pp. 366–379, March, 1990.

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Ol'shanetskii, M.A. Quantum-mechanical calculation of the orders of finite simple groups of lie type. Theor Math Phys 82, 256–266 (1990). https://doi.org/10.1007/BF01029219

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