Tomáš Salač (2012)
Archivum Mathematicum
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The Penrose transform gives an isomorphism between the kernel of the -Dirac operator over an affine subset and the third sheaf cohomology group on the twistor space. In the paper we give an integral formula which realizes the isomorphism and decompose the kernel as a module of the Levi factor of the parabolic subgroup. This gives a new insight into the structure of the kernel of the operator.
Čap, Andreas, Souček, Vladimír (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Todor Milev, Petr Somberg (2013)
Archivum Mathematicum
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The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras , and generalized conformal -Verma modules of scalar type. As a result, we classify the -singular vectors for this class of -modules.
Vít Tuček (2012)
Archivum Mathematicum
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We show that the conformally invariant Yamabe operator on a complex conformal manifold can be constructed as a first BGG operator by inducing from certain infinite-dimensional representation.
Laurent Manivel, Dennis M. Snow (1996)
Compositio Mathematica
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Zbyněk Šír (2001)
Commentationes Mathematicae Universitatis Carolinae
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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.