Geodesic
Quantum-mechanical calculation of the orders of finite simple groups of Lie type
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 3, pp. 366-379 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of the class of invariant quantum systems on Lie algebras whose partition functions for fixed temperatures can be expressed in terms of the orders of finite simple groups of Lie type constructed from the original Lie algebras. 
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     title = {Quantum-mechanical calculation of~the orders of~finite simple groups {of~Lie} type},
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M. A. Olshanetsky. Quantum-mechanical calculation of the orders of finite simple groups of Lie type. Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 3, pp. 366-379. http://geodesic.mathdoc.fr/item/TMF_1990_82_3_a4/

[1] Gorenstein D., Konechnye prostye gruppy, Mir, M., 1985 | MR | Zbl

[2] Daison F., Statisticheskaya teoriya energeticheskikh urovnei slozhnykh sistem, IL, M., 1963

[3] Rocha-Caridi A., Vertex Operators in Mathematics and Physics, eds. J. Lepovsky, S. Mandelstam, I. Singer, Springer-Verlag, N. Y., 1983 | MR | Zbl

[4] Gross D. J., Harvey J. A., Martinec E., Rohm R., Nucl. Phys., B256 (1985), 253–284 | DOI

[5] Gepner D., Witten E., Nucl. Phys., B278 (1986), 493 | DOI | MR

[6] Kac V. G., Infinite dimensional Lie algebras, Cambridge University Press, 1985 | MR | Zbl

[7] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl

[8] Hamidi Sh., Vafa C., Nucl. Phys., B279 (1987), 465–513 | DOI | MR

[9] Coxeter H. S. M., Ann. Math., 35 (1934), 588 | DOI | MR

[10] Springer T., Teoriya invariantov, Mir, M., 1981 | MR | Zbl

[11] Serr Zh.-P., Kurs arifmetiki, Mir, M., 1972 | MR | Zbl

[12] Anderson G., Moore G., Rationality in Conformal Field Theory, Preprint IASSNS-HEP-87/69, Princeton Univ., 1987 | MR

[13] Olshanetsky M. A., Perelomov A. M., Phys. Rep., 94 (1983), 313–404 | DOI | MR

[14] Shephard G. C., Todd J. A., Canad. J. Math., 6 (1954), 274–304 ; Cohen A. M., Ann. Scient. Ec. Norm. Sup., 4 (1976), 379–436 | DOI | MR | Zbl | DOI | MR | Zbl

[15] Manin Yu. I., Reflections on Arithmetical Physics, Talk at the Poiana-Brasov School on Strings and Conformal Field Theory, 1987

[16] Knezer M., “Poluprostye algebraicheskie gruppy”, Algebraicheskaya teoriya chisel, Mir, M., 1969; Гельфанд И. М., Граев М. И., Пятецкий-Шапиро И. И., Теория представлений и автоморфные функции, Наука, М., 1966 | MR

[17] Witten E., Topological sigma-model, Preprint IAS-PUB-SNS-HEP 88/7, Princeton Univ., 1988 | MR | Zbl