Science in China Series A: Mathematics

, Volume 40, Issue 7, pp 687–696 | Cite as

The inverse Abel transform for an exceptional bounded symmetric domain

  • Fuliu Zhu


By using the first shift operator of thebc 2- root system, the elementary spherical functions on the exceptional bounded symmetric domainE 6/spin(10) ×T are obtained, and the inverse Abel transform for this space is derived. Finally an expression of the heat kernel of this domain is given.


exceptional bounded symmetric domain shift operator inverse Abel transforin heat kernel 


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  1. 1.
    Zhu Fuliu, On the inverse Abel transform for certain Riemannian symmetric spaces of rank 2,Math. Ann., 1996, 305: 617.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Meaney, C., The inverse Abel transform for SU(p, q),Ark. Math., 1984, 24: 131.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Lohoue, N., Zhu Fuliu, Estimation faible de certaines fonctions rnaximales,C. R. Acad. Sci. Paris, 1986, série I: 303.Google Scholar
  4. 4.
    Helgason, S.,Differential Geometry, Lie Groups and Symmetric Spaces, New York: Academic Press, 1978.MATHGoogle Scholar
  5. 5.
    Helgason, S.,Groups and Geometric Analysis, New York: Academic Press, 1984.MATHGoogle Scholar
  6. 6.
    Ise, M., Bounded symmetric domains of exceptional,J. Fac. Univ. Tokyo, 1976, 23: 75.MATHMathSciNetGoogle Scholar
  7. 7.
    Drucker, D., Exceptional Lie algebras and the structure of Hermitian symmetric spaces,Mem. Amer. Math. Soc., 1978, 208.Google Scholar
  8. 8.
    Opdam, E., Root systems and the rnultivariable hypergeometric functions III,Camp. Math., 1988, 67: 21.MATHMathSciNetGoogle Scholar
  9. 9.
    Hba, A., Sur 1’ inversion de la transformation d’ Abel et les fonctions sph’eriques,Th]`ese docteur d’ Etar, Université de Nice, 1988.Google Scholar
  10. 10.
    Rouvière, F., Sur la transformation d’ Abel des groups de Lie semisimple de rang un,Ann. Scula. Norm. Sup., Pisa, 1983, 101, 263.Google Scholar
  11. 11.
    Anker, J. P., Le noyau de la chaleur sur les espaces symetriques U(p, q)/U(p) X U(q),Lect. Notes in Math., Vol. 1359, Berlin: Springer-Verlag, 1988.Google Scholar

Copyright information

© Science in China Press 1997

Authors and Affiliations

  • Fuliu Zhu
    • 1
  1. 1.Department of MathematicsWuhan UniversityWuhanChina

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