Abstract
In this chapter we recall from [14, 15, 21, 22] a method based on the Fourier transform (F-method) to find explicit formulæ of differential symmetry breaking operators. For our purpose we need to develop the F-method for matrix-valued operators. A new ingredient is a canonical decomposition of the algebraic Fourier transform of the vector-valued principal series representations into the “scalar part” involving differential operators of higher order and into the “vector part” of first order. This is formulated and proved in Sect. 3.4.
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© 2016 Springer Nature Singapore Pte Ltd.
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Kobayashi, T., Kubo, T., Pevzner, M. (2016). F-method for Matrix-Valued Differential Operators. In: Conformal Symmetry Breaking Operators for Differential Forms on Spheres. Lecture Notes in Mathematics, vol 2170. Springer, Singapore. https://doi.org/10.1007/978-981-10-2657-7_3
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DOI: https://doi.org/10.1007/978-981-10-2657-7_3
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