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.
Keywords
- Vector Bundle
- Parabolic Subgroup
- Weyl Algebra
- Vector Part
- Vector Bundle Versus
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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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Publisher Name: Springer, Singapore
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Online ISBN: 978-981-10-2657-7
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