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Through differentiable cohomology are induced Fréchet G - modules that construct the irreducible G - modules of infinite dimension, whose cohomology of infinite dimension representations is applicable to the Langlands classification obtaining the corresponding unitary representations. The obtained extensions are developed with u-cohomology and intertwining operators of induced representations applicable to certain Langlands data and through sheaves of holomorphic bundles. After are realized applications in the geometrical Langlands program to field theory and their ramifications in derived geometry. In this book are included several research exercises and research projects that can be developed in postgraduate courses and PhD dissertations.

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Doctorate in Mathematics with PhD thesis: Some relations Between the Cohomological Induction of Vogan-Zuckerman and the Langlands Classification.Editor-in-Chief of Journal of Mathematics in USA.Postdocs in Cuba and Russia: Geometrical Langlands Program and Infinite Lie Theory. Head of Research Department TESCHA.Authority in QED & Nanotechnology

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