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Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 2009, Volume 151, Book 4, Pages 15–35 (Mi uzku763)  

This article is cited in 5 scientific papers (total in 5 papers)

The Laplace Operator Spectrum on Compact Simply Connected Rank Two Lie Groups

V. N. Berestovskii, V. M. Svirkin

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science

Abstract: In the paper, we suggest an algorithm for calculation of the Laplace operator spectrum for real-valued functions defined on a compact simply connected simple Lie group with a bi-invariant Riemannian metric and establish a connection of the Ricci curvature of this metric with the spectrum. By means of the algorithm suggested and with the use of results of the number theory and the theory of integral binary quadratic forms, an explicit calculation of the spectrum for all compact simply connected simple Lie groups of rank two is given.

Keywords: Laplace operator, spectrum, group representation, Killing form, Ricci curvature.

Full text: PDF file (335 kB)
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UDC: 514.764.227+514.765+517.984.56+511
Received: 12.08.2009

Citation: V. N. Berestovskii, V. M. Svirkin, “The Laplace Operator Spectrum on Compact Simply Connected Rank Two Lie Groups”, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 151, no. 4, Kazan University, Kazan, 2009, 15–35

Citation in format AMSBIB
\Bibitem{BerSvi09}
\by V.~N.~Berestovskii, V.~M.~Svirkin
\paper The Laplace Operator Spectrum on Compact Simply Connected Rank Two Lie Groups
\serial Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki
\yr 2009
\vol 151
\issue 4
\pages 15--35
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku763}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Svirkin, “Spektr operatora Laplasa svyaznykh kompaktnykh prostykh grupp Li ranga odin i dva”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 152, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2010, 219–234  mathnet  mathscinet  elib
    2. V. N. Berestovskiǐ, “Zonal spherical functions on CROSS's and special functions”, Siberian Math. J., 53:4 (2012), 611–624  mathnet  crossref  mathscinet  isi
    3. V. N. Berestovskii, I. A. Zubareva, V. M. Svirkin, “The spectra of the Laplace operators on connected compact simple Lie groups of rank 3”, Siberian Adv. Math., 26:3 (2016), 153–181  mathnet  crossref  crossref  mathscinet  elib
    4. I. A. Zubareva, “The spectrum of the Laplace operator on connected compact simple Lie groups of rank four”, Siberian Adv. Math., 27:3 (2017), 196–226  mathnet  crossref  crossref  elib
    5. I. A. Zubareva, “Spektr operatora Laplasa na nekotorykh svyaznykh kompaktnykh prostykh gruppakh Li ranga chetyre. II”, Matem. tr., 22:2 (2019), 34–53  mathnet  crossref
  • Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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