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Eigenvalues of matrices of complex representations of finite groups of lie type

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Algebra Some Current Trends

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1352))

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References

  1. T.R. Berger, Hall-Higman type theorems, IV. Proc. Amer. Math. Soc. 37 (1973), 317–325.

    Article  MathSciNet  MATH  Google Scholar 

  2. H.F. Blichfeldt, Finite collineation groups, Univ. Chicago Press, Chicago, 1917.

    Google Scholar 

  3. C.W. Curtis, W.M. Kantor and G.M. Seitz, The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc. 218 (1976), 1–59.

    MathSciNet  MATH  Google Scholar 

  4. W. Feit and J. Tits, Projective representations of minimum degree of group extensions, Can. J. Math. 30 (1978), 1092–1102.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Feit and J. Thompson, Finite groups which have a faithful representation of degree less than (p-1)/2, Pacific J. Math. 11 (1961), 1257–1262.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ph. Hall and G. Higman, On the p-length of p-soluble groups and reduction theorems for Burnside's problem, Proc. London Math. Soc. 6 (1956), 1–42.

    Article  MathSciNet  MATH  Google Scholar 

  7. Ch. Hering, Transitive linear groups and linear groups which contain irreducible subgroups of prime order, J. Algebra 93 (1985), 151–164.

    Article  MathSciNet  MATH  Google Scholar 

  8. C.Y. Ho, On quadratic pairs, J. Algebra 43 (1976), 338–358.

    Article  MathSciNet  MATH  Google Scholar 

  9. V. Landazuri and G. Seitz, On the minimal degree of projective representations of the finite Chevalley groups, J. Algebra 32 (1974), 418–443.

    Article  MathSciNet  MATH  Google Scholar 

  10. A.A. Premet, The weights of irreducible rational representations of semisimple algebraic groups over a field of prime characteristic (in Russian), Mat. Sb. 133 (175) (1987), 167–183. (English. translation: Math. USSR, Sb.).

    Google Scholar 

  11. G.M. Seitz, Some representations of classical groups, J. London Math. Soc. 10 (1975), 115–120.

    Article  MathSciNet  MATH  Google Scholar 

  12. E. Shult, On groups admitting fixed point free abelian operator groups, Illinois J. Math. 9 (1965), 701–720.

    MathSciNet  MATH  Google Scholar 

  13. R. Steinberg, Lectures on Chevalley groups, mimeographed lecture notes, Yale Univ. Math. Dept. (1968).

    Google Scholar 

  14. R. Steinberg, Representations of algebraic groups, Nagoya J. Math. 22 (1963), 33–56.

    Article  MathSciNet  MATH  Google Scholar 

  15. D.A. Suprunenko, Soluble and nilpotent linear groups (in Russian), Minsk, 1958. (English translation: Amer. Math. Soc., Providence, R.I., 1963.)

    Google Scholar 

  16. J. Thompson, Quadratic pairs, Proc. Intern. Congr. Math. (Nice, 1970), Vol. 1, Gauthier-Villars, Paris (1971), 375–376.

    MATH  Google Scholar 

  17. F.D. Veldcamp, Representations of algebraic groups of type F4 in characteristic 2, J. Algebra 16 (1970), 326–339.

    Article  MathSciNet  Google Scholar 

  18. H.N. Ward, Representations of symplectic groups, J. Algebra 20 (1972), 182–195.

    Article  MathSciNet  MATH  Google Scholar 

  19. A.E. Zalesskii, Normalizer of an extraspecial linear group (in Russian), Vestsi Akad. Navuk BSSR, Ser. fiz.-mat. navuk, 6 (1985), 11–16.

    MathSciNet  Google Scholar 

  20. A.E. Zalesskii, Spectra of elements of order p in complex representations of finite Chevalley groups of characteristic p (in Russian) Vestsi Akad. Navuk BSSR, Ser. fiz.-mat. navuk, 6, (1986), 20–25.

    MathSciNet  Google Scholar 

  21. A.E. Zalesskii, Fixed points of elements of order p in complex representations of finite Chevalley groups of characteristic p (in Russian), Dokl. Akad. Nauk BSSR, 31 (1987), 104–107.

    MathSciNet  Google Scholar 

  22. A.E. Zalesskii, Eigenvalue 1 of matrices of complex representations of finite Chevalley groups, (in Russian), Trudy Mat. Inst. AN SSSR, 187 (1988) (to appear) (English translation: Proc. Steklov Inst. Math.).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of Byelorussian SSR, 220604, Minsk, USSR

    A. E. Zalesskii

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  1. A. E. Zalesskii
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Luchezar L. Avramov Kerope B. Tchakerian

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© 1988 Springer-Verlag

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Zalesskii, A.E. (1988). Eigenvalues of matrices of complex representations of finite groups of lie type. In: Avramov, L.L., Tchakerian, K.B. (eds) Algebra Some Current Trends. Lecture Notes in Mathematics, vol 1352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082027

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  • DOI: https://doi.org/10.1007/BFb0082027

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50371-2

  • Online ISBN: 978-3-540-45994-1

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