LAUSR

The classical Rankin–Cohen brackets are bi-differential operators from $$C^\infty ({\mathbb {R}})\times C^\infty ({\mathbb {R}})$$ C ∞ ( R ) × C ∞ ( R ) into $$ C^\infty ({\mathbb {R}})$$ C ∞ ( R ) . They are covariant for the (diagonal) action of $$\mathrm{SL}(2,{\mathbb {R}})$$ SL ( 2 , R ) through principal series representations. We construct generalizations of these operators, replacing $${\mathbb {R}}$$ R by $${\mathbb {R}}^n,$$ R n , the group $$\mathrm{SL}(2,{\mathbb {R}})$$ SL ( 2 , R ) by the group $$\mathrm{SO}_0(1,n+1)$$ SO 0 ( 1 , n + 1 ) viewed as the conformal group of $${\mathbb {R}}^n,$$ R n , and functions by differential forms.