TITLE:
Derived Categories in Langlands Geometrical Ramifications: Approaching by Penrose Transforms
AUTHORS:
Francisco Bulnes
KEYWORDS:
Geometrical Langlands Correspondence, Hecke Categories, Moduli Stacks, Penrose Transforms, Quasi-Coherent Sheaves
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.6,
June
13,
2014
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.)