The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations in the belonging cohomological context such as H^0 (g[[z] ],V_critical )=C[Op_LG (D^X)] which is natural in the framework of the integral transforms to the generalizing of the Zuckerman functors that will be useful to the obtaining of the different factors of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field (Verma modules) and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category H_(G^^ ) ∞ on an adequate moduli stack and the holomorphic L_(G-) bundles category with a special connection (Deligne connection). The corresponding 〖D 〗_-modules may be viewed as sheaves of conformal blocks (or co-invariants) (images under a generalized version of the Penrose transform) naturally arising in the framework of conformal field theory.
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Pure and Applied Mathematics Journal (Volume 3, Issue 6-2)
This article belongs to the Special Issue Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program |
DOI | 10.11648/j.pamj.s.2014030602.11 |
Page(s) | 1-5 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2014. Published by Science Publishing Group |
Langlands Correspondence, Hecke Sheaves Category, Moduli Stacks, Ramifications, Twisted 〖D 〗_- Modules, Verma Module Extensions
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APA Style
Francisco Bulnes. (2014). Integral Geometry Methods on Deformed Categories in Field Theory II. Pure and Applied Mathematics Journal, 3(6-2), 1-5. https://doi.org/10.11648/j.pamj.s.2014030602.11
ACS Style
Francisco Bulnes. Integral Geometry Methods on Deformed Categories in Field Theory II. Pure Appl. Math. J. 2014, 3(6-2), 1-5. doi: 10.11648/j.pamj.s.2014030602.11
AMA Style
Francisco Bulnes. Integral Geometry Methods on Deformed Categories in Field Theory II. Pure Appl Math J. 2014;3(6-2):1-5. doi: 10.11648/j.pamj.s.2014030602.11
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TY - JOUR T1 - Integral Geometry Methods on Deformed Categories in Field Theory II AU - Francisco Bulnes Y1 - 2014/10/24 PY - 2014 N1 - https://doi.org/10.11648/j.pamj.s.2014030602.11 DO - 10.11648/j.pamj.s.2014030602.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 5 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2014030602.11 AB - The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations in the belonging cohomological context such as H^0 (g[[z] ],V_critical )=C[Op_LG (D^X)] which is natural in the framework of the integral transforms to the generalizing of the Zuckerman functors that will be useful to the obtaining of the different factors of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field (Verma modules) and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category H_(G^^ ) ∞ on an adequate moduli stack and the holomorphic L_(G-) bundles category with a special connection (Deligne connection). The corresponding 〖D 〗_-modules may be viewed as sheaves of conformal blocks (or co-invariants) (images under a generalized version of the Penrose transform) naturally arising in the framework of conformal field theory. VL - 3 IS - 6-2 ER -