A representation-theoretical proof of Bransonʼs classification of elliptic generalized gradients

The purpose of this paper is to present a new proof of Bransonʼs classification (Branson, 1997 [3]), of minimal elliptic sums of generalized gradients. The advantage of this proof is that it is local, being mainly based on representation theory and on the relationship between ellipticity and refined Kato inequalities. This approach is promising for the classification of elliptic generalized gradients of G-structures, for other subgroups G of the special orthogonal group.