Volume 3, Issue 6-2, December 2014, Page: 26-29
The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules
Francisco Bulnes, Head of Research Department in Mathematics and Engineering, TESCHA, Chalco, Mexico
Kubo Watanabe, Researcher in Department of Mathematics, Osaka University, Osaka, Japan
Ronin Goborov, Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia
Received: Nov. 22, 2014;       Accepted: Nov. 27, 2014;       Published: Nov. 29, 2014
DOI: 10.11648/j.pamj.s.2014030602.15      View  2943      Downloads  87
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.
Curved Differential Operators, Deformed Category, Extended Functor, Generalized Verma Modules, Harish-Chandra Category, Recillas’s Conjecture
To cite this article
Francisco Bulnes, Kubo Watanabe, Ronin Goborov, The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules, Pure and Applied Mathematics Journal. Special Issue: Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program. Vol. 3, No. 6-2, 2014, pp. 26-29. doi: 10.11648/j.pamj.s.2014030602.15
E. G. Kalnins, W. Miller, “The Theory of the Wave Equation in Space-Time. II. The Group ”SIAM J. Math. Anal., 9(1), pp12–33.
J. Lepowski, “A generalization of the Bernstein-Gelfand-Gelfand resolution,” J. Algebra, 49 (1977), 496-511.
C. R. LeBrun, Twistors, ambitwistors and conformal gravity, Twistor in Physics, Cambridge, UK, 1981.
S. Gindikin, Penrose transform at flag domains, The Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse (Wien Austria), Vol. 9, 1978, pp.A-1090.
J. W. Rice, Cousin complexes and resolutions of representations, The Penrose Transform and Analytic Cohomology in Representation Theory, Eastwood, M. Wolf, J. Zierau R (eds.), American Mathematical Society, 1993.
F. Bulnes, Cohomology of Moduli Spaces in Differential Operators Classification to the Field Theory (II), in: Proceedings of Function Spaces, Differential Operators and Non-linear Analysis., 2011, Tabarz Thur, Germany, Vol. 1 (12) pp001-022.
R. Penrose, Solutions of the zero-rest-mass equations, J. Mathematical Phys., Vol. 10, 1969, pp. 38-39.
F. Bulnes, M. Shapiro, “On a General Integral Operators Theory to Geometry and Analysis,” IMUNAM, SEPI-IPN, México, 2007.
F. Bulnes, Integral geometry and complex integral operators cohomology in field theory on space-time, in: Proceedings of 1st International Congress of Applied Mathematics-UPVT (Mexico)., 2009, vol. 1, Government of State of Mexico, pp. 42-51.
F. Bulnes, On the last progress of cohomological induction in the problem of classification of Lie groups representations, Proceedings of Masterful Conferences. International Conference of Infinite Dimensional Analysis and Topology (Ivano-Frankivsk, Ukraine). Vol. 1, 2009, pp. 21.
A. W. Knapp, N. Wallach, “Szego Kernels Associated with Discrete Series,” Inv. Mat. Vol. 34, 1976, pp. 163-200.
S. Gindikin, “The Penrose Transform and Complex Integral Geometry Problems,” Modern Problems of Mathematics (Moscow), Vol. 17, 1981, pp. 57-112.
W. Schmid, “Homogeneous Complex Manifolds and Representations of Semisimple Lie Groups,” Surveys Monograph (University of California, Berkeley, C. A) Aer. Math. Soc., ed. Vol. 31, 1967, pp. 233-286.
L. Barchini, A. W. Knapp, and R. Zierau, J. Funct. Anal. 107 (1992), 302-341.
S. Schröer, Some Calabi-Yau threefolds with obstructed deformations over the Witt vectors, AMS, Mathematics Subject Classification, Vol. 14J28, 14J30, 14J32, 14K10, 1991.
C. R. Graham, Non existence of curved conformally invariant operators, Preprint, 1980.
F. Bulnes, Research on Curvature of Homogeneous Spaces, 1st ed.; TESCHA: State of Mexico, Mexico, 2010; pp. 44-66.
M. Kashiwara, “Representation Theory and D-Modules on Flag Varieties,” Astérisque 9 (1989) no. 173-174, 55-109.
P. Shapira, A. D’Agnolo, “Radon-Penrose Transform for D-Modules, Elsevier Holland 2 (1996), no. 139, 349-382.
D. Skinner, L. Mason, Heterotic twistor-string theory, Oxford University, 2007.
F. Bulnes, Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory, Journal of Mathematics and System Sciences, David Publishing, USA Vol. 3, no.10, pp491-507.
F. Bulnes, Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory, Advances in Pure Mathematics 3 (2) (2013) 246-253. doi: 10.4236/apm.2013.32035.
R. J. Baston, M. G. Eastwood, The Penrose transform, Oxford University Press, New York, 1989.
A. Kapustin, M. Kreuser and K. G. Schlesinger, Homological mirror symmetry: New Developments and Perspectives, Springer. Berlin, Heidelberg, 2009.
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