## T. Kobayashi, T. Kubo, and M. Pevzner.
*Conformal Symmetry Breaking Operators for Differential Forms on
Spheres*, volume 2170 of *
Lecture Notes in Mathematics*.
Springer Singapore, 2016. ix+192 pages.
DOI:
10.1007/978-981-10-2657-7. arXiv:
1605.09272. Softcover ISBN: 978-981-10-2656-0. eBook ISBN:
978-981-10-2657-7..

We give a complete classification of
conformally covariant differential operators between the spaces of *i*-forms on the sphere *S*^{n} and *j*-forms on the totally geodesic hypersphere *S*^{n-1}.
Moreover, we find explicit formulæ for
these new matrix-valued operators in the flat coordinates
in terms of basic operators in differential geometry and classical
orthogonal polynomials.
We also establish matrix-valued factorization identities
among all possible combinations of conformally covariant differential operators.
The main machinery of the proof is the “F-method" based on the
“algebraic Fourier transform of Verma modules"
(Kobayashi-Pevzner [Selecta Math. 2016])
and its extension to matrix-valued case developed here.
A short summary of the main results was announced in
[C. R. Acad. Sci. Paris, 2016].

[ DOI |
arXiv |
SpringerLink ]

© Toshiyuki Kobayashi