About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Šír, Zbyněk
Properties of operators occurring in the Penrose transform. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 42 (2001), issue 4, pp. 681-690
MSC: 32L25, 53C28 | MR 1883377 | Zbl 1090.53504
Keywords:
Penrose transform; conformally invariant operators
Summary:
It is shown that operators occurring in the classical Penrose transform are differential. These operators are identified depending on line bundles over the twistor space.
References:
Baston R.J., Eastwood M.G.: The Penrose Transform and its Interaction with Representation Theory. Oxford University Press (1989). MR 1038279
Buchdahl N.P.: On the relative de Rham sequence. Proc. Amer. Math. Soc. 87 (1983), 363-366. MR 0681850 | Zbl 0511.58001
Eastwood M.G.: A duality for homogeneous bundles on twistor space. J. London Math. Soc. 31 (1985), 349-356. MR 0809956 | Zbl 0534.14008
Griffiths P., Harris J.: Principles of Algebraic Geometry. A Wiley-Intescience Publication (1978). MR 0507725 | Zbl 0408.14001
Gunning R.C., Rossi H.: Analytic Functions of Several Complex Variables. Prentice-Hall (1965). MR 0180696 | Zbl 0141.08601
Rocha-Cardini A.: Splitting criteria for $\mathfrak g$-modules induced from parabolic and the Bernstain-Gelfand-Gelfand resolution of a finite dimensional, irreducible $\mathfrak g$-module. Trans. Amer. Math. Soc. (1980), 262 335-361. MR 0586721
Slovák J.: Natural operators on conformal manifolds. Dissertation (1994), Masaryk University Brno. MR 1255551
Ward R.S., Wells R.O.: Twistor Geometry and Field Theory. Cambridge University Press (1983). MR 1054377
Partner of
EuDML logo