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The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules

Received: 22 November 2014     Accepted: 27 November 2014     Published: 29 November 2014
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Abstract

The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes of sheaves of differential operators to their classification) of Verma modules as classifying spaces of these differential operators and their corresponding integrals through of geometrical integral transforms.

Published in 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.2014030602.15
Page(s) 26-29
Creative Commons

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.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Curved Differential Operators, Deformed Category, Extended Functor, Generalized Verma Modules, Harish-Chandra Category, Recillas’s Conjecture

References
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[3] C. R. LeBrun, Twistors, ambitwistors and conformal gravity, Twistor in Physics, Cambridge, UK, 1981.
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Cite This Article
  • APA Style

    Francisco Bulnes, Kubo Watanabe, Ronin Goborov. (2014). The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules. Pure and Applied Mathematics Journal, 3(6-2), 26-29. https://doi.org/10.11648/j.pamj.s.2014030602.15

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    ACS Style

    Francisco Bulnes; Kubo Watanabe; Ronin Goborov. The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules. Pure Appl. Math. J. 2014, 3(6-2), 26-29. doi: 10.11648/j.pamj.s.2014030602.15

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    AMA Style

    Francisco Bulnes, Kubo Watanabe, Ronin Goborov. The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules. Pure Appl Math J. 2014;3(6-2):26-29. doi: 10.11648/j.pamj.s.2014030602.15

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  • @article{10.11648/j.pamj.s.2014030602.15,
      author = {Francisco Bulnes and Kubo Watanabe and Ronin Goborov},
      title = {The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules},
      journal = {Pure and Applied Mathematics Journal},
      volume = {3},
      number = {6-2},
      pages = {26-29},
      doi = {10.11648/j.pamj.s.2014030602.15},
      url = {https://doi.org/10.11648/j.pamj.s.2014030602.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030602.15},
      abstract = {The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes of sheaves of differential operators to their classification) of Verma modules as classifying spaces of these differential operators and their corresponding integrals through of geometrical integral transforms.},
     year = {2014}
    }
    

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    AB  - The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes of sheaves of differential operators to their classification) of Verma modules as classifying spaces of these differential operators and their corresponding integrals through of geometrical integral transforms.
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Author Information
  • Head of Research Department in Mathematics and Engineering, TESCHA, Chalco, Mexico

  • Researcher in Department of Mathematics, Osaka University, Osaka, Japan

  • Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia

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