Properties of operators occurring in the Penrose transform

Zbyněk Šír

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 4, page 681-690
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Šír, Zbyněk. "Properties of operators occurring in the Penrose transform." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 681-690. <http://eudml.org/doc/248823>.

@article{Šír2001,
abstract = {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.},
author = {Šír, Zbyněk},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Penrose transform; conformally invariant operators; Penrose transform; conformally invariant operators},
language = {eng},
number = {4},
pages = {681-690},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Properties of operators occurring in the Penrose transform},
url = {http://eudml.org/doc/248823},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Šír, Zbyněk
TI - Properties of operators occurring in the Penrose transform
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 4
SP - 681
EP - 690
AB - 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.
LA - eng
KW - Penrose transform; conformally invariant operators; Penrose transform; conformally invariant operators
UR - http://eudml.org/doc/248823
ER -

References

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  1. Baston R.J., Eastwood M.G., The Penrose Transform and its Interaction with Representation Theory, Oxford University Press (1989). (1989) MR1038279
  2. Buchdahl N.P., On the relative de Rham sequence, Proc. Amer. Math. Soc. 87 (1983), 363-366. (1983) Zbl0511.58001MR0681850
  3. Eastwood M.G., A duality for homogeneous bundles on twistor space, J. London Math. Soc. 31 (1985), 349-356. (1985) Zbl0534.14008MR0809956
  4. Griffiths P., Harris J., Principles of Algebraic Geometry, A Wiley-Intescience Publication (1978). (1978) Zbl0408.14001MR0507725
  5. Gunning R.C., Rossi H., Analytic Functions of Several Complex Variables, Prentice-Hall (1965). (1965) Zbl0141.08601MR0180696
  6. Rocha-Cardini A., Splitting criteria for 𝔤 -modules induced from parabolic and the Bernstain-Gelfand-Gelfand resolution of a finite dimensional, irreducible 𝔤 -module, Trans. Amer. Math. Soc. (1980), 262 335-361. (1980) MR0586721
  7. Slovák J., Natural operators on conformal manifolds, Dissertation (1994), Masaryk University Brno. (1994) MR1255551
  8. Ward R.S., Wells R.O., Twistor Geometry and Field Theory, Cambridge University Press (1983). (1983) MR1054377

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