  In this paper we prove local analytic hypoellipticity for a degenerate sum of
squares of complex vector fields generalizing those of Kohn in "Hypoellipticity
and Loss of Derivatives". Kohn's article is to appear in the Annals of
Mathematics with an appendix by Derridj and Tartakoff proving local analyticity
in that case. Here we consider vector fields corresponding to a CR manifold of
finite type so there is a kind of double degeneracy, and prove local
analyticity using our balanced localization of high derivatives in the
"missing" direction T. In a forthcoming paper, Bove, Derridj, Kohn and
Tartakoff will use these techniques to prove hypoellipticity for both classes
of operators.
