Differential symmetry breaking operators: I. General theory and F-method
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Toshiyuki Kobayashi [1] ; Michael Pevzner [2]
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[1] University of Tokyo
University of Tokyo
Japón
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[2] University of Reims Champagne-Ardenne
University of Reims Champagne-Ardenne
Arrondissement de Reims, Francia
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 801-845
- Idioma: inglés
- Enlaces
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Resumen
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.
