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The Spectrum of the Laplace Operator on Connected Compact Simple Lie Groups of Rank Four. II

Abstract

In the present article, we explicitly compute the spectrum of the Laplace operator on smooth real-valued and complex-valued functions on connected compact simple Lie groups of rank four with a bi-invariant Riemannian metrics that correspond to the root systems \(A_4 \) and \(F_4 \).

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REFERENCES

  1. 1

    V. N. Berestovskiĭ and V. M. Svirkin, “The Laplace operator on normal homogeneous Riemannian manifolds,” Mat. Trudy 12, no. 2, 3 (2009) [Siberian Adv. Math. 20, 231 (2010)].

    MathSciNet  Article  Google Scholar 

  2. 2

    V. N. Berestovskiĭ and V. M. Svirkin, “The spectrum of the Laplace operator on compact simply connected Lie groups of rank two,” Uch. Zap. Kazan Gos. Univ., Ser. Fiz.-Mat. Nauki 151:4, 15 (2009) [in Russian].

    MATH  Google Scholar 

  3. 3

    V. N. Berestovskiĭ, I. A. Zubareva, and V. M. Svirkin, “The spectra of the Laplace operators on connected compact simple Lie groups of rank 3,” Mat. Trudy19, no. 1, 3 (2016) [Siberian Adv. Math. 26, 153 (2016)].

    MathSciNet  Article  Google Scholar 

  4. 4

    N. Bourbaki, Éléments de Mathématique. Groupes et Algèbres de Lie. Chapitres IV, V et VI (Hermann, Paris, 1968). [Elements of mathematics. Lie groups and Lie algebras. Chapters 4–6 (Springer, Berlin, 2002)].

  5. 5

    V. M. Svirkin, “Spectrum of the Laplace operator on connected compact simple Lie groups of rank one or two,” Uch. Zap. Kazan Gos. Univ., Ser. Fiz.-Mat. Nauki152:1, 219 (2010) [in Russian].

    MathSciNet  MATH  Google Scholar 

  6. 6

    I. A. Zubareva, “The spectrum of the Laplace operator on connected compact simple Lie groups of rank four,” Mat. Trudy 19, no. 2, 42 (2016) [Siberian Adv. Math. 27, 196 (2017)].

    MathSciNet  Article  Google Scholar 

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ACKNOWLEDGMENTS

The author is grateful to Professor V. N. Berestovskiĭ for formulation of the problem and his useful comments.

Funding

The work was supported by the program of fundamental scientific research of the Siberian Branch of the Russian Academy of Sciences, No. I.1.4 (project No. 0314-2016-0004).

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Correspondence to I. A. Zubareva.

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Zubareva, I.A. The Spectrum of the Laplace Operator on Connected Compact Simple Lie Groups of Rank Four. II. Sib. Adv. Math. 30, 213–227 (2020). https://doi.org/10.3103/S1055134420030062

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Keywords

  • Laplace operator
  • spectrum
  • group representation
  • Killing form
  • Ricci curvature