Advertisement

Inventiones mathematicae

, Volume 112, Issue 1, pp 657–664 | Cite as

Jordan algebras and Capelli identities

  • Bertram Kostant
  • Siddhartha Sahi
Article

Keywords

Jordan Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B] Boe, B.: Homomorphisms between generalized Verma modules. Trans. Am. Math. Soc.288, 791–799 (1985)Google Scholar
  2. [BK] Braun, H., Koecher, M.: Jordan-Algebren. Berlin Heidelberg New York: Springer 1966Google Scholar
  3. [FK] Faraut, J. Koranyi, A.: Function spaces and reproducing kernels on bounded symmetric domains. J. Funct. Anal.88, 64–89 (1990)Google Scholar
  4. [G] Guillemonat, A.: On some semi-spherical representations of a Hermitian symmetric pair of tubular type. Math. Ann.246, 93–116 (1980)Google Scholar
  5. [H] Helgason, S.: Groups and Geometric Analysis. New York: Academic Press 1984Google Scholar
  6. [Hu] Humphreys, J.: Introduction to Lie Algebras and Representation Theory. Berlin Heidelberg New York: Springer 1972Google Scholar
  7. [JV] Jakobsen, H., Vergne, M.: Wave and Dirac operators and representations of the conformal groups. J. Funct. Anal.24, 52–106 (1977)Google Scholar
  8. [J] Johnson, K.: Degenerate principal series and compact groups. Math. Ann.287, 703–718 (1990)Google Scholar
  9. [K1] Koecher, M.: Über eine Gruppe von rationalen Abbildungen. Invent. Math.3, 136–171 (1967)Google Scholar
  10. [K2] Koecher, M.: Imbeddings of Jordan algebras into Lie algebras I. Am. J. Math.89, 787–816 (1967), II. ibid. Koecher, M.: Imbeddings of Jordan algebras into Lie algebras I. Am. J. Math.90, 476–510 (1968)Google Scholar
  11. [Kos] Kostant, B.: On the existence and irreducibility of certain series of representations. In: Gelfand, I.M. (ed.): Lie Groups and their Representations. New York: Halsted Press 1975Google Scholar
  12. [KS] Kostant, B., Sahi, S.: The Capelli identity, tube domains and the generalized Laplace transform. Adv. Math.87, 71–92 (1991)Google Scholar
  13. [L] Loos, O.: Jordan triple systems,R-spaces and bounded symmetric domains. Bull. Am. Math. Soc.77, 558–561 (1971)Google Scholar
  14. [M] Moore, C.: Compactifications of symmetric domains II. The Cartan domains. Am. J. Math.86, 358–378 (1964)Google Scholar
  15. [N] Nagano, T.: Transformation groups on compact symmetric spaces. Trans. Am. Math. Soc.118, 428–453 (1965)Google Scholar
  16. [S1] Sahi, S.: The Capelli identity and unitary representations. Compos. Math.81, 247–260 (1992)Google Scholar
  17. [S2] Sahi, S.: Unitary representations on the Shilov boundary of a symmetric tube domain. In: Representations of Groups and Algebras (Contemp. Math. vol. 145). Providence: Am. Math. Soc. 1993Google Scholar
  18. [S3] Sahi, S.: Explicit Hilbert spaces for certain unipotent representations. Invent. Math.110, 409–418 (1992)Google Scholar
  19. [Sat] Satake, I.: Algebraic Structures of Symmetric Domains. (Pub. Math. Soc. Japan vol. 14). Princeton: Princeton University Press 1980Google Scholar
  20. [Sp] Springer, T.: Jordan Algebras and Algebraic Groups. (Erg. Math. vol. 75) Berlin Heidelberg New York: Springer 1973Google Scholar
  21. [T] Takeuchi, M.: Cell decompositions and Morse equalities on certain symmetric spaces. J. Fac. Sci. Univ. Tokyo Sect. I12, 81–192 (1965)Google Scholar
  22. [Ti] Tits, J.: Une classe d'algébres de Lie en relation avec les algébres de Jordan. Indag. Math.24 [= Proc. Ned. Akad. Wet. Ser. A65] 530–535 (1962)Google Scholar
  23. [V] Vogan, D.: Singular unitary representations. In: Non-Commutative Harmonic Analysis and Lie groups (Lect. Notes Math. vol. 880, pp. 506–535) Berlin Heidelberg New York: Springer 1980Google Scholar
  24. [W1] Wallach, N.: The analytic continuation of the discrete series II. Trans. Am. Math. Soc.251, 19–37 (1979)Google Scholar
  25. [W2] Wallach, N.: Polynomial differential operators associated with Hermitian symmetric spaces. In: Representation Theory of Lie Groups and Lie Algebras, pp. 76–94 Singapore: World Scientific 1992Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Bertram Kostant
    • 1
  • Siddhartha Sahi
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

Personalised recommendations