A Geometric Interpretation and Explicit Form for Higher-order Hankel Operators

where x(z) = ∑∞ j=1 xjz j is the symbol of the operator. In terms of the Hardy polarization of odd spinors on S, B1(x) = P+MxP−, where P+, P− are projections and Mx is the multiplication operator corresponding to x. The map x 7−→ B1(x) is conformally equivariant in a sense explained in §2. In this paper we derive explicit expressions for certain well-known higher-order generalizations of this map, which are also conformally equivariant. Indeed, we will prove Theorem 1.1. The higher-order Hankel operator of order s + 1 with symbol x(z)(dz), where x(z) = ∑∞ j=s+1 xjz , has the formula Bs+1(x) = P+Ls(x)P−, where Ls(x) is the differential operator Ls(x) = s ∑