Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Second order conformal covariants

Author: Thomas Branson
Journal: Proc. Amer. Math. Soc. 126 (1998), 1031-1042
MSC (1991): Primary 47F05
MathSciNet review: 1422849
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We complete the classification of second order, bundle valued differential operator invariants of Riemannian and pseudo-Riemannian conformal structure, by classifying such operators which pass between bundles associated to different representations of the rotation or spin group.

References [Enhancements On Off] (What's this?)

  • 1. R. J. Baston, Verma modules and differential conformal invariants, J. Differential Geom. 32 (1990), no. 3, 851–898. MR 1078164
  • 2. R. J. Baston and M. G. Eastwood, Invariant operators, Twistors in mathematics and physics, London Math. Soc. Lecture Note Ser., vol. 156, Cambridge Univ. Press, Cambridge, 1990, pp. 129–163. MR 1089914
  • 3. C. Bennett and T. Branson, Curvature actions, in preparation.
  • 4. Thomas P. Branson, Conformally covariant equations on differential forms, Comm. Partial Differential Equations 7 (1982), no. 4, 393–431. MR 652815, 10.1080/03605308208820228
  • 5. Thomas P. Branson, Differential operators canonically associated to a conformal structure, Math. Scand. 57 (1985), no. 2, 293–345. MR 832360
  • 6. T. Branson, Nonlinear phenomena in the spectral theory of geometric linear differential operators, Proc. Symp. Pure Math. 59 (1996), 27-65. CMP 96:13
  • 7. T. Branson, Stein-Weiss operators and ellipticity, J. Funct. Anal., to appear.
  • 8. R. Brauer, Sur la multiplication des caractéristiques des groupes continus et semi-simples, C.R. Acad. Sci. Paris 204 (1937), 1784-1786.
  • 9. H. D. Fegan, Conformally invariant first order differential operators, Quart. J. Math. Oxford (2) 27 (1976), no. 107, 371–378. MR 0482879
  • 10. Hans Freudenthal, Zur Berechnung der Charaktere der halbeinfachen Lieschen Gruppen. I, II, Nederl. Akad. Wetensch. Proc. Ser. A. 57 = Indag. Math. 16 (1954), 369–376, 487–491 (German). MR 0067123
  • 11. R. Jenne, A construction of conformally invariant differential operators, Ph.D. dissertation, University of Washington, 1988.
  • 12. Bertram Kostant, A formula for the multiplicity of a weight, Trans. Amer. Math. Soc. 93 (1959), 53–73. MR 0109192, 10.1090/S0002-9947-1959-0109192-6
  • 13. S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds, preprint, 1983.
  • 14. J. Slovák, Invariant operators on conformal manifolds, lecture notes, University of Vienna, 1992, archived at file://
  • 15. E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163–196. MR 0223492
  • 16. H. Weyl, The Classical Groups: Their Invariants and Representations, Princeton University Press, Princeton, 1939.
  • 17. Volkmar Wünsch, On conformally invariant differential operators, Math. Nachr. 129 (1986), 269–281. MR 864639, 10.1002/mana.19861290123

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47F05

Retrieve articles in all journals with MSC (1991): 47F05

Additional Information

Thomas Branson
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242

Received by editor(s): September 3, 1996
Additional Notes: Research partially supported by NSF grant INT-9114401
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society