Abstract
Singletons and twistors are unified from a group-theoretic point of view. In particular, singletons are described as the de Sitter analogue of twistors.
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DiracP. A. M., A remarkable representation of the 3+2 de Sitter group, J. Math. Phys. 4, 901–909 (1963).
EnrightT., HoweR., and WallachN., A classification of unitary highest weight modules, in P. C.Trombi (ed.), Representation Theory of Reductive Groups, Birkhäuser, Boston, 1983.
FerberA., Supertwistors and conformal supersymmetry, Nucl. Phys. B132, 55–64 (1978).
FlatoM. and FronsdalC., One massless particle equals two Dirac singletons, Lett. Math. Phys. 2, 421–426 (1978).
FlatoM. and FronsdalC., Quantum field theory of singletons. The Rac, J. Math. Phys. 22, 1100–1105 (1981).
FlatoM. and FronsdalC., The singleton dipole, Commun. Math. Phys. 108, 469–482 (1987).
FronsdalC., The super singleton I: Free Dipole and Interactions at Infinity, Lett. Math. Phys. 16, 163–172 (1988).
Gel'fandI. M., GindikinS. G., and GreevM. I., Integral geometry in affine and projective spaces, Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki 16, 53–226 (1980). Engl. trans.: J. Soviet Math. 18, 39–167 (1982).
GunaydinM., NilssonB. E. W., SierraG., and TownsendP. K., Singletons and superstrings, Phys. Lett. B176, 45–49 (1986).
Harish-Chandra, Representations of Semisimple Lie Groups: IV. Amer. J. Math. 77, 743–777 (1955); V. Amer. J. Math. 78, 1–41 (1956); VI. Amer. J. Math. 78, 564–628 (1956).
HeidenreichW., Quantum theory of Spin-1/2 fields with gauge freedom, Nuovo Cim. 80A, 220–240 (1984).
HelgasonS., Groups and Geometric Analysis, Academic Press, Orlandon, Florida, 1984.
JakobsenH., Hermitian symmetric spaces and their unitary highest weight modules, J. Funct. Anal. 52, 385–412 (1983).
JakobsenH., Basic covariant differential operators on Hermitian symmetric spaces, Ann. Sci. de l'Ecole Normale Supérieure, Quatrième Série 18, 421–436 (1985).
JakobsenH., Subspace structure of holomorphic representations, Matematisk-fysiske Meddelelsed 41, 1–22 (1985).
JakobsenH. and VergneM., Wave and Dirac operators, and representations of the conformal group, J. Funct. Anal. 24, 52–106 (1977).
KnappA. and OkamotoK., Limits of the holomorphic discrete series, J. Funct. Anal. 9, 375–409 (1972).
ManinYu., Flag superspaces and supersymmetric Yang-Mills equations, in Artin and Tate (eds.), Arithmetic and Geometry, Vol. 2, Birkhäuser, Boston, 1983.
Nakashima, M., Indefinite harmonic forms and gauge theory, Commun. Math. Phys., to be published.
NicolaiH. and SezginE., Singleton representations of Osp(N, 4), Phys. Lett., B143, 389–395 (1984).
PercocoU., The spin-1/2 singleton dipole, Lett. Math. Phys. 12, 315–322 (1986).
RawnsleyJ., SchmidW., and WolfJ., Singular unitary, representations and indefinite harmonic forms, J. Funct. Anal. 51, 1–114 (1983).
Schmid, W., Boundary value problems for group invariant differential equations, Asterique, hors serie, 311–321 (1985).
SekiguchiJ., Eigenspaces of the Laplace-Beltrami operator on a hyperboloid, Nagoya Math. J. 79, 151–185 (1980).
VergneM. and RossiH., Analytic continuation of the holomorphic discrete series of a semi-simple Lie group, Acta Math. 136, 1–59 (1976).
WellsR., Complex manifolds and mathematical physics, Bull. A.M.S. 1, 296–336 (1979).
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Nakashima, M. Singletons and twistors. Lett Math Phys 16, 237–244 (1988). https://doi.org/10.1007/BF00398960
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DOI: https://doi.org/10.1007/BF00398960