DIFFERENTIAL SYMMETRY BREAKING OPERATORS. I. GENERAL THEORY AND F-METHOD

Abstract : We prove a one-to-one correspondence between differential symmetry breaking operators for equivariant vector bundles over two homogeneous spaces and certain homomorphisms for representations of two Lie algebras, in connection with branching problems of the restriction of representations. We develop a new method (F-method) based on the algebraic Fourier transform for generalized Verma modules, which characterizes differential symmetry breaking operators by means of certain systems of partial differential equations. In contrast to the setting of real flag varieties, continuous symmetry breaking operators of Hermitian symmetric spaces are proved to be differential operators in the holomorphic setting. In this case symmetry breaking operators are characterized by differential equations of second order via the F-method.
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Selecta Mathematica (New Series), Springer Verlag, 2016, 22 (2), pp.801 - 845. 〈10.1007/s00029-015-0207-9〉
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https://hal.archives-ouvertes.fr/hal-01907210
Contributeur : Michael Pevzner <>
Soumis le : dimanche 28 octobre 2018 - 17:17:23
Dernière modification le : jeudi 8 novembre 2018 - 01:16:09

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Toshiyuki Kobayashi, Michael Pevzner. DIFFERENTIAL SYMMETRY BREAKING OPERATORS. I. GENERAL THEORY AND F-METHOD. Selecta Mathematica (New Series), Springer Verlag, 2016, 22 (2), pp.801 - 845. 〈10.1007/s00029-015-0207-9〉. 〈hal-01907210〉

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