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Penrose Transform on Induced *D _{G/H}*-Modules and Their Moduli Stacks in the Field Theory

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We consider generalizations of the Radon-Schmid transform on coherent *D*_{G/H}-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (*D*-Modules) characterizing conformal classes in the space-time that determine a space moduli [1] on coherent sheaves for the securing solutions in field theory [2]. In a major context, elements of derived categories like *D*-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets [3]) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding Hecke category.

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*D*-Modules and Their Moduli Stacks in the Field Theory,"

_{G/H}*Advances in Pure Mathematics*, Vol. 3 No. 2, 2013, pp. 246-253. doi: 10.4236/apm.2013.32035.

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