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Article Dans Une Revue Selecta Mathematica (New Series) Année : 2016

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

Résumé

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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Dates et versions

hal-01907210 , version 1 (28-10-2018)

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

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