Geodesic
The spectra of the Laplace operators on connected compact simple Lie groups of rank 3
Matematičeskie trudy, Tome 19 (2016) no. 1, pp. 3-45 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We expose explicit calculations of the spectra of the Laplace operators for smooth real or complex functions on all connected compact simple Lie groups of rank 3 with bi-invariant Riemannian metric and establish the relationship of the obtained formulas with number theory and integer-valued ternary and binary quadratic forms. 
@article{MT_2016_19_1_a0,
     author = {V. N. Berestovskii and I. A. Zubareva and V. M. Svirkin},
     title = {The spectra of the {Laplace} operators on connected compact simple {Lie} groups of rank~3},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--45},
     year = {2016},
     volume = {19},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2016_19_1_a0/}
}
TY  - JOUR
AU  - V. N. Berestovskii
AU  - I. A. Zubareva
AU  - V. M. Svirkin
TI  - The spectra of the Laplace operators on connected compact simple Lie groups of rank 3
JO  - Matematičeskie trudy
PY  - 2016
SP  - 3
EP  - 45
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MT_2016_19_1_a0/
LA  - ru
ID  - MT_2016_19_1_a0
ER  - 
%0 Journal Article
%A V. N. Berestovskii
%A I. A. Zubareva
%A V. M. Svirkin
%T The spectra of the Laplace operators on connected compact simple Lie groups of rank 3
%J Matematičeskie trudy
%D 2016
%P 3-45
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/MT_2016_19_1_a0/
%G ru
%F MT_2016_19_1_a0
V. N. Berestovskii; I. A. Zubareva; V. M. Svirkin. The spectra of the Laplace operators on connected compact simple Lie groups of rank 3. Matematičeskie trudy, Tome 19 (2016) no. 1, pp. 3-45. http://geodesic.mathdoc.fr/item/MT_2016_19_1_a0/

[1] Adams Dzh., Lektsii po gruppam Li, Nauka, M., 1979 | MR

[2] Berestovskii V. N., “O spektre operatora Laplasa dlya veschestvennykh funktsii na kompaktnykh normalnykh odnorodnykh rimanovykh mnogoobraziyakh”, Dni geometrii v Novosibirske-2011, Tr. mezhdunar. konf., posvyaschennoi 50-letiyu kafedry geometrii i topologii Novosibirskogo gos. un-ta, Izd-vo NGU, Novosibirsk, 2012, 16–28

[3] Berestovskii V. N., “Zonalnye sfericheskie funktsii na KROSPakh i spetsialnye funktsii”, Sib. matem. zhurn., 53:4 (2012), 765–780 | MR | Zbl

[4] Berestovskii V. N., Svirkin V. M., “Operator Laplasa na odnorodnykh normalnykh rimanovykh mnogoobraziyakh”, Matem. tr., 12:2 (2009), 3–40 | MR

[5] Berestovskii V. N., Svirkin V. M., “Spektr operatora Laplasa na kompaktnykh odnosvyaznykh prostykh gruppakh Li ranga dva”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki., 151:4 (2009), 15–35 | Zbl

[6] Burbaki N., Gruppy i algebry Li, v. IV–VI, Mir, M., 1972 | MR

[7] Bukhshtab A. A., Teoriya chisel, Gos. uch.-ped. izdat., M., 1960

[8] Venkov B. A., Elementarnaya teoriya chisel, Ob'ed. nauch.-tekhn. izd-vo NKTP SSSR, M.–L., 1937

[9] Dynkin E. B., Onischik A. L., “Kompaktnye gruppy Li v tselom”, UMN, 10:4(66) (1955), 3–74 | MR | Zbl

[10] Devenport G., Vysshaya arifmetika. Vvedenie v teoriyu chisel, Nauka, M., 1965

[11] Konvei Dzh., Sloen N., Upakovki sharov, reshetki i gruppy, v. 1, 2, Mir, M., 1990

[12] G. P. Matvievskaya, E. P. Ozhigova i dr. (sost.), Neopublikovannye materialy L. Eilera po teorii chisel, ed. Nevskaya N. I., Nauka, SPb, 1997

[13] Svirkin V. M., “Spektr operatora Laplasa svyaznykh kompaktnykh prostykh grupp Li ranga odin i dva”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 152:1 (2010), 219–234 | MR | Zbl

[14] Cartan E., “Les groupes projectifs qui ne laissent invariante aucune multiplicity plane”, Bull. Soc. Math. France, 41 (1913), 53–94 | MR

[15] Conway J. H., The Sensual Quadratic Form, The Carus Mathematical Monographs, 26, The Mathematical Association of America, Washington, DC, 1997 | MR | Zbl

[16] Onishchik A. L., Lectures on Real Semisimple Lie Algebras and Their Representations, ESI Lectures in Mathematics and Physics, European Math. Soc. Publishing House, Zurich, Switzerland, 2004 | MR | Zbl