## T. Kobayashi and M. Pevzner.
Rankin-Cohen operators for symmetric pairs.
preprint, 53 pp.
arXiv:1301.2111.

Rankin-Cohen bidifferential operators are the projectors onto irreducible summands in the decomposition of the tensor product of two representations of *SL*(2,**R**). We consider the general problem to find explicit formulæ for such projectors
in the setting of multiplicity-free branching laws for reductive symmetric pairs.
For this purpose we develop a new method (F-method) based on an *algebraic
Fourier transform for generalized Verma modules*, which enables us to characterize those
projectors by means of certain systems of partial differential
equations of second order.

As an application of the F-method we give a solution to the initial problem by constructing equivariant
holomorphic differential operators explicitly for all symmetric
pairs of split rank one and reveal an intrinsic reason why the coefficients of Jacobi polynomials appear
in these operators including the classical Rankin-Cohen brackets as a special
case.

[ arXiv |
IHES-preprint |
preprint version(pdf) |
enlarged version into two papers: PART1, PART2 ]

© Toshiyuki Kobayashi