The classical Rankin–Cohen brackets are bi-differential operators from C∞(R) × C∞(R) into C∞(R). They are covariant for the (diagonal) action of SL (2 , R) through principal series representations. We construct generalizations of these operators, replacing R by Rn, the group SL (2 , R) by the group SO (1 , n+ 1) viewed as the conformal group of Rn, and functions by differential forms.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics