Abstract
Some derived categories and their deformed versions are used to develop a theory of the ramifications of field studied in the geometrical Langlands program to obtain the correspondences between moduli stacks and solution classes represented cohomologically under the study of the kernels of the differential operators studied in their classification of the corresponding field equations. The corresponding D-modules in this case may be viewed as sheaves of conformal blocks (or co-invariants) (images under a version of the Penrose transform) naturally arising in the framework of conformal field theory. Inside the geometrical Langlands correspondence and in their cohomological context of strings can be established a framework of the space-time through the different versions of the Penrose transforms and their relation between them by intertwining operators (integral transforms that are isomorphisms between cohomological spaces of orbital spaces of the space-time), obtaining the functors that give equivalences of their corresponding categories.(For more information,please refer to the PDF version.)
Highlights
IntroductionThe extensions given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic L G - bundles category with a special connection (Deligne connection), establish a viewing of the D - modules as sheaves of conformal blocks (or co-invariants) (images under a version of the Penrose transform [1]-[3]) naturally arising in the framework of conformal field theory
The extensions given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic L G - bundles category with a special connection (Deligne connection), establish a viewing of the D - modules as sheaves of conformal blocks naturally arising in the framework of conformal field theory
Likewise the duality between string theories stay established through of the intertwining operators of the Penrose transform in all different dualities field/particle and the conformally and holonomy levels required in invariance of the space-time field theory. we can explain the relation between certain branes and twisted D - modules on the space
Summary
The extensions given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic L G - bundles category with a special connection (Deligne connection), establish a viewing of the D - modules as sheaves of conformal blocks (or co-invariants) (images under a version of the Penrose transform [1]-[3]) naturally arising in the framework of conformal field theory. We can to say, that the techniques of localization functors used to produce global categories of Hecke eigensheaves from local categories using the technique of integral transform is accord with the Langlands data structure given by the affine Hecke categories [8] [9], which are required to conform a representation theory of affine Kac-Moody algebras that will complete the research on geometrical Langlands correspondence
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