A Representation-Theoretic Criterion for Local Solvability of Left Invariant Differential Operators on Nilpotent Lie Groups

Abstract

Let L be a left invariant differential operator on the nilpotent Lie group N. It is shown that if tr(L) is invertible for all irreducible representations it in general position (and if the inverses satisfy some mild technical conditions), then L is locally solvable.This result genera'izes a theorem of L. Rothschild.